On the solvability of the homogeneous Neumann problem for second order uniformly elliptic equations on non-smooth domains

ilustraciones, diagramas

Autores:
Guerra Gutiérrez, Juan Sebastián
Tipo de recurso:
Fecha de publicación:
2024
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
eng
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oai:repositorio.unal.edu.co:unal/86714
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/86714
https://repositorio.unal.edu.co/
Palabra clave:
510 - Matemáticas::515 - Análisis
510 - Matemáticas::512 - Álgebra
ALGEBRAS DE VON NEUMANN
ECUACIONES DIFERENCIALES-PROBLEMAS, EJERCICIOS, ETC.
TEORIA DE LOS OPERADORES
ESPACIOS FUNCIONALES
ESPACIOS DE SOBOLEV
Von Neumann algebras
Differential equations - problems, exercises, etc.
Operator theory
Function spaces
Sobolev spaces
Problema de Neumann
Ecuaciones Ddferenciales parciales
Operador uniformemente elíptico
Dominios no-regulares
Neumann problem
Partial differential equations
Uniformly elliptic operator
Non-smooth domains
Rights
openAccess
License
Reconocimiento 4.0 Internacional
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oai_identifier_str oai:repositorio.unal.edu.co:unal/86714
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.eng.fl_str_mv On the solvability of the homogeneous Neumann problem for second order uniformly elliptic equations on non-smooth domains
dc.title.translated.spa.fl_str_mv Caracterización de la solubilidad del problema de Neumann con condiciones de frontera homogéneas para ecuaciones uniformemente elípticas de segundo orden sobre dominios generales
title On the solvability of the homogeneous Neumann problem for second order uniformly elliptic equations on non-smooth domains
spellingShingle On the solvability of the homogeneous Neumann problem for second order uniformly elliptic equations on non-smooth domains
510 - Matemáticas::515 - Análisis
510 - Matemáticas::512 - Álgebra
ALGEBRAS DE VON NEUMANN
ECUACIONES DIFERENCIALES-PROBLEMAS, EJERCICIOS, ETC.
TEORIA DE LOS OPERADORES
ESPACIOS FUNCIONALES
ESPACIOS DE SOBOLEV
Von Neumann algebras
Differential equations - problems, exercises, etc.
Operator theory
Function spaces
Sobolev spaces
Problema de Neumann
Ecuaciones Ddferenciales parciales
Operador uniformemente elíptico
Dominios no-regulares
Neumann problem
Partial differential equations
Uniformly elliptic operator
Non-smooth domains
title_short On the solvability of the homogeneous Neumann problem for second order uniformly elliptic equations on non-smooth domains
title_full On the solvability of the homogeneous Neumann problem for second order uniformly elliptic equations on non-smooth domains
title_fullStr On the solvability of the homogeneous Neumann problem for second order uniformly elliptic equations on non-smooth domains
title_full_unstemmed On the solvability of the homogeneous Neumann problem for second order uniformly elliptic equations on non-smooth domains
title_sort On the solvability of the homogeneous Neumann problem for second order uniformly elliptic equations on non-smooth domains
dc.creator.fl_str_mv Guerra Gutiérrez, Juan Sebastián
dc.contributor.advisor.spa.fl_str_mv Ardila de la Peña, Víctor Manuel
dc.contributor.author.spa.fl_str_mv Guerra Gutiérrez, Juan Sebastián
dc.subject.ddc.spa.fl_str_mv 510 - Matemáticas::515 - Análisis
510 - Matemáticas::512 - Álgebra
topic 510 - Matemáticas::515 - Análisis
510 - Matemáticas::512 - Álgebra
ALGEBRAS DE VON NEUMANN
ECUACIONES DIFERENCIALES-PROBLEMAS, EJERCICIOS, ETC.
TEORIA DE LOS OPERADORES
ESPACIOS FUNCIONALES
ESPACIOS DE SOBOLEV
Von Neumann algebras
Differential equations - problems, exercises, etc.
Operator theory
Function spaces
Sobolev spaces
Problema de Neumann
Ecuaciones Ddferenciales parciales
Operador uniformemente elíptico
Dominios no-regulares
Neumann problem
Partial differential equations
Uniformly elliptic operator
Non-smooth domains
dc.subject.lemb.spa.fl_str_mv ALGEBRAS DE VON NEUMANN
ECUACIONES DIFERENCIALES-PROBLEMAS, EJERCICIOS, ETC.
TEORIA DE LOS OPERADORES
ESPACIOS FUNCIONALES
ESPACIOS DE SOBOLEV
dc.subject.lemb.eng.fl_str_mv Von Neumann algebras
Differential equations - problems, exercises, etc.
Operator theory
Function spaces
Sobolev spaces
dc.subject.proposal.spa.fl_str_mv Problema de Neumann
Ecuaciones Ddferenciales parciales
Operador uniformemente elíptico
Dominios no-regulares
dc.subject.proposal.eng.fl_str_mv Neumann problem
Partial differential equations
Uniformly elliptic operator
Non-smooth domains
description ilustraciones, diagramas
publishDate 2024
dc.date.accessioned.none.fl_str_mv 2024-08-09T13:17:25Z
dc.date.available.none.fl_str_mv 2024-08-09T13:17:25Z
dc.date.issued.none.fl_str_mv 2024
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TM
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/86714
dc.identifier.instname.spa.fl_str_mv Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv https://repositorio.unal.edu.co/
url https://repositorio.unal.edu.co/handle/unal/86714
https://repositorio.unal.edu.co/
identifier_str_mv Universidad Nacional de Colombia
Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.references.spa.fl_str_mv Brezis, H. (2011). Functional analysis, Sobolev spaces and partial differential equations. Springer.
Courant, R., John, F., Blank, A. A., and Solomon, A. (1974). Introduction to calculus and analysis, volume 2. A Wiley-Interscience Publication.
Kesavan, S. (1989). Topics in functional analysis and applications. New Age International Ltd., Publishers.
Kesavan, S. (2009). Functional analysis. Hindustan Book Agency.
Krantz, S. G. and Parks, H. R. (2008). Geometric integration theory. Birkhäuser.
Krasnoselskii and Rutickii, Y. B. (1961). Convex functions and Orlicz spaces. P. Noordhoff LTD- Groningen.
Kreyszig, E. (1978). Introductory functional analysis with applications. John Wiley & Sons.
Leoni, G. (2009). A first course in Sobolev spaces. American Mathematical Society.
Kufner, A., Maligranda, L., and Persson, L.-E. (2006). The Prehistory of the Hardy Inequality. The American Mathematical Monthly, 113(8), 715–732.
Maz’ya, V. (1968). On neumann’s problem in domains with nonregular boundaries. Siberian Mathematical Journal, 9, 990–1012.
Maz’ya, V. G. (1973). On certain integral inequalities for functions of many variables. Journal of Soviet Mathematics, 1(2), 205–234
Maz’ya, V. G. (2011). Sobolev Spaces: With Applications to Elliptic Partial Differential Equations. Springer.
Movahedi-Lankarani, H. (1992). On the theorem of Rademacher. Real Analysis Exchange, 17(2), 802 – 808.
Nandakumaran, A. and Datti, P. (2020). Partial differential equations: classical theory with a modern touch. Cambridge University Press.
Natanson, I. P. (1964). Theory of functions of a real variable, volume 1. Courier Dover Publications.
Rana, I. K. (2002). An introduction to measure and integration. American Mathematical Society.
Rektorys, K. (1977). Variational methods in mathematics, science and engineering. Reidel Publishing Company.
Rossmann, J., Takac, P., and Wildenhain, G. (2012). The Maz’ya Anniversary Collection: Volume 1: On Maz’ya’s work in functional analysis, partial differential equations and applications, volume 109. Birkhäuser.
Rudin, W. (1973). Functional analysis. McGraw-Hill Book Company.
Rudin, W. (1987). Real and complex analysis. McGraw-Hill International Editions.
Villani, A. (1985). Another note on the inclusion lp(μ) ⊂ lq(μ). The American Mathematical Monthly, 92(7), 485–487.
Kondrat’ev, V. A. and Oleinik, O. A. (1983). Boundary-value problems for partial differential equations in non-smooth domains. Russian Mathematical Surveys, 38(2):1–86
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dc.rights.license.spa.fl_str_mv Reconocimiento 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento 4.0 Internacional
http://creativecommons.org/licenses/by/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.spa.fl_str_mv viii, 106 páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv Bogotá - Ciencias - Maestría en Ciencias - Matemáticas
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv Bogotá, Colombia
dc.publisher.branch.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá
institution Universidad Nacional de Colombia
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spelling Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Ardila de la Peña, Víctor Manuelae8f73196b28451ab2ca2d84f77df280Guerra Gutiérrez, Juan Sebastián9f358402276a84014ce6c8b6e3ccec1c2024-08-09T13:17:25Z2024-08-09T13:17:25Z2024https://repositorio.unal.edu.co/handle/unal/86714Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramasWe give solvability criteria for the weak formulation of the homogeneous Neumann problem for uniformly elliptic operators of the form \begin{ceqn} \begin{align*} \mathcal{L}u = - \displaystyle \sum_{i,j = 1}^n \frac{\partial}{\partial x_j}\left( a_{ij}\dfrac{\partial u}{\partial x_i}\right)+au \end{align*} \end{ceqn} where the $a_{ij}$ and $a$ are measurable functions satisfying certain adequate hypotheses. Conditions on the domain of definition are given to ensure the solvability of the problem in which smoothing restrictions on the boundary are relaxed.Damos criterios de solubilidad de la formulación débil del problema homogéneo de Neumann para operadores uniformemente elípticos de la forma \begin{ceqn} \begin{align*} \mathcal{L}u = - \displaystyle \sum_{i,j = 1}^n \frac{\partial}{\partial x_j}\left( a_{ij}\dfrac{\partial u}{\partial x_i}\right)+au \end{align*} \end{ceqn} donde las $a_{ij}$ y $a$ son funciones medibles que satisfacen ciertas hipótesis. Se establecen condiciones sobre el dominio de definición que garantizan la solubilidad del problema y que relajan restricciones de suavidad en la frontera (Texto tomado de la fuente).MaestríaMagíster en Ciencias - MatemáticasEcuaciones diferenciales parcialesviii, 106 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::515 - Análisis510 - Matemáticas::512 - ÁlgebraALGEBRAS DE VON NEUMANNECUACIONES DIFERENCIALES-PROBLEMAS, EJERCICIOS, ETC.TEORIA DE LOS OPERADORESESPACIOS FUNCIONALESESPACIOS DE SOBOLEVVon Neumann algebrasDifferential equations - problems, exercises, etc.Operator theoryFunction spacesSobolev spacesProblema de NeumannEcuaciones Ddferenciales parcialesOperador uniformemente elípticoDominios no-regularesNeumann problemPartial differential equationsUniformly elliptic operatorNon-smooth domainsOn the solvability of the homogeneous Neumann problem for second order uniformly elliptic equations on non-smooth domainsCaracterización de la solubilidad del problema de Neumann con condiciones de frontera homogéneas para ecuaciones uniformemente elípticas de segundo orden sobre dominios generalesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMBrezis, H. (2011). Functional analysis, Sobolev spaces and partial differential equations. Springer.Courant, R., John, F., Blank, A. A., and Solomon, A. (1974). Introduction to calculus and analysis, volume 2. A Wiley-Interscience Publication.Kesavan, S. (1989). Topics in functional analysis and applications. New Age International Ltd., Publishers.Kesavan, S. (2009). Functional analysis. Hindustan Book Agency.Krantz, S. G. and Parks, H. R. (2008). Geometric integration theory. Birkhäuser.Krasnoselskii and Rutickii, Y. B. (1961). Convex functions and Orlicz spaces. P. Noordhoff LTD- Groningen.Kreyszig, E. (1978). Introductory functional analysis with applications. John Wiley & Sons.Leoni, G. (2009). A first course in Sobolev spaces. American Mathematical Society.Kufner, A., Maligranda, L., and Persson, L.-E. (2006). The Prehistory of the Hardy Inequality. The American Mathematical Monthly, 113(8), 715–732.Maz’ya, V. (1968). On neumann’s problem in domains with nonregular boundaries. Siberian Mathematical Journal, 9, 990–1012.Maz’ya, V. G. (1973). On certain integral inequalities for functions of many variables. Journal of Soviet Mathematics, 1(2), 205–234Maz’ya, V. G. (2011). Sobolev Spaces: With Applications to Elliptic Partial Differential Equations. Springer.Movahedi-Lankarani, H. (1992). On the theorem of Rademacher. Real Analysis Exchange, 17(2), 802 – 808.Nandakumaran, A. and Datti, P. (2020). Partial differential equations: classical theory with a modern touch. Cambridge University Press.Natanson, I. P. (1964). Theory of functions of a real variable, volume 1. Courier Dover Publications.Rana, I. K. (2002). An introduction to measure and integration. American Mathematical Society.Rektorys, K. (1977). Variational methods in mathematics, science and engineering. Reidel Publishing Company.Rossmann, J., Takac, P., and Wildenhain, G. (2012). The Maz’ya Anniversary Collection: Volume 1: On Maz’ya’s work in functional analysis, partial differential equations and applications, volume 109. Birkhäuser.Rudin, W. (1973). Functional analysis. McGraw-Hill Book Company.Rudin, W. (1987). Real and complex analysis. McGraw-Hill International Editions.Villani, A. (1985). Another note on the inclusion lp(μ) ⊂ lq(μ). The American Mathematical Monthly, 92(7), 485–487.Kondrat’ev, V. A. and Oleinik, O. A. (1983). Boundary-value problems for partial differential equations in non-smooth domains. Russian Mathematical Surveys, 38(2):1–86EstudiantesInvestigadoresMaestrosPúblico generalLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/86714/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51ORIGINAL1015413807.2024.pdf1015413807.2024.pdfTesis de Maestría en Matemáticasapplication/pdf1363306https://repositorio.unal.edu.co/bitstream/unal/86714/2/1015413807.2024.pdf9401170673d07aae59437bffbb0f0fd1MD52THUMBNAIL1015413807.2024.pdf.jpg1015413807.2024.pdf.jpgGenerated Thumbnailimage/jpeg4634https://repositorio.unal.edu.co/bitstream/unal/86714/3/1015413807.2024.pdf.jpg32253507f9c0bc1e5794b0dd1c4c6b18MD53unal/86714oai:repositorio.unal.edu.co:unal/867142024-08-27 23:11:21.176Repositorio Institucional Universidad Nacional de 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