Homogenization of a parabolic Dirichlet problem by a method of Dahlberg
Consider the linear parabolic operator in divergence form Hu := ∂tu(X, t) - div(A(X)∇u(X, t)). We employ a method of Dahlberg to show that the Dirichlet problem for H in the upper half plane is well-posed for boundary data in Lp, for any elliptic matrix of coefficients A which is periodic and satisf...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:191239 |
| Acceso en línea: | https://ddd.uab.cat/record/191239 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6221805 |
| Access Level: | acceso abierto |
| Palabra clave: | Second order parabolic operator Dirichlet problem Homogenization |
| Sumario: | Consider the linear parabolic operator in divergence form Hu := ∂tu(X, t) - div(A(X)∇u(X, t)). We employ a method of Dahlberg to show that the Dirichlet problem for H in the upper half plane is well-posed for boundary data in Lp, for any elliptic matrix of coefficients A which is periodic and satisfies a Dini-type condition. This result allows us to treat a homogenization problem for the equation ∂tuε(X, t) - div(A(X/ε)∇uε(X, t)) in Lipschitz domains with Lp-boundary data. |
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