Matches in SemOpenAlex for { <https://semopenalex.org/work/W2801407835> ?p ?o ?g. }
Showing items 1 to 62 of
62
with 100 items per page.
- W2801407835 endingPage "100" @default.
- W2801407835 startingPage "61" @default.
- W2801407835 abstract "For bounded domains Ω , we prove that the L p -norm of a regular function with compact support is controlled by weighted L p -norms of its gradient, where the weight belongs to a class of symmetric non-negative definite matrix-valued functions. The class of weights is defined by regularity assumptions and structural conditions on the degeneracy set , where the determinant vanishes. In particular, the weight A is assumed to have rank at least 1 when restricted to the normal bundle of the degeneracy set S . This generalization of the classical Poincaré inequality is then applied to develop a robust theory of first-order L p -based Sobolev spaces with matrix-valued weight A . The Poincaré inequality and these Sobolev spaces are then applied to produce various results on existence, uniqueness and qualitative properties of weak solutions to boundary-value problems for degenerate elliptic , degenerate parabolic and degenerate hyperbolic partial differential equations (PDEs) of second order written in divergence form, where A is calibrated to the matrix of coefficients of the second-order spatial derivatives. The notion of weak solution is variational : the spatial states belong to the matrix-weighted Sobolev spaces with p = 2. For the degenerate elliptic PDEs, the Dirichlet problem is treated by the use of the Poincaré inequality and Lax–Milgram theorem, while the treatment of the Cauchy–Dirichlet problem for the degenerate evolution equations relies only on the Poincaré inequality and the parabolic and hyperbolic counterparts of the Lax–Milgram theorem." @default.
- W2801407835 created "2018-05-17" @default.
- W2801407835 creator A5053674909 @default.
- W2801407835 creator A5064788920 @default.
- W2801407835 creator A5079884024 @default.
- W2801407835 date "2018-04-22" @default.
- W2801407835 modified "2023-09-26" @default.
- W2801407835 title "Poincaré inequalities for Sobolev spaces with matrix-valued weights and applications to degenerate partial differential equations" @default.
- W2801407835 doi "https://doi.org/10.1017/s0308210517000427" @default.
- W2801407835 hasPublicationYear "2018" @default.
- W2801407835 type Work @default.
- W2801407835 sameAs 2801407835 @default.
- W2801407835 citedByCount "10" @default.
- W2801407835 countsByYear W28014078352018 @default.
- W2801407835 countsByYear W28014078352019 @default.
- W2801407835 countsByYear W28014078352020 @default.
- W2801407835 countsByYear W28014078352021 @default.
- W2801407835 countsByYear W28014078352022 @default.
- W2801407835 crossrefType "journal-article" @default.
- W2801407835 hasAuthorship W2801407835A5053674909 @default.
- W2801407835 hasAuthorship W2801407835A5064788920 @default.
- W2801407835 hasAuthorship W2801407835A5079884024 @default.
- W2801407835 hasBestOaLocation W28014078352 @default.
- W2801407835 hasConcept C121332964 @default.
- W2801407835 hasConcept C134306372 @default.
- W2801407835 hasConcept C185644265 @default.
- W2801407835 hasConcept C202444582 @default.
- W2801407835 hasConcept C33923547 @default.
- W2801407835 hasConcept C62520636 @default.
- W2801407835 hasConcept C72319582 @default.
- W2801407835 hasConcept C99730327 @default.
- W2801407835 hasConceptScore W2801407835C121332964 @default.
- W2801407835 hasConceptScore W2801407835C134306372 @default.
- W2801407835 hasConceptScore W2801407835C185644265 @default.
- W2801407835 hasConceptScore W2801407835C202444582 @default.
- W2801407835 hasConceptScore W2801407835C33923547 @default.
- W2801407835 hasConceptScore W2801407835C62520636 @default.
- W2801407835 hasConceptScore W2801407835C72319582 @default.
- W2801407835 hasConceptScore W2801407835C99730327 @default.
- W2801407835 hasIssue "1" @default.
- W2801407835 hasLocation W28014078351 @default.
- W2801407835 hasLocation W28014078352 @default.
- W2801407835 hasLocation W28014078353 @default.
- W2801407835 hasOpenAccess W2801407835 @default.
- W2801407835 hasPrimaryLocation W28014078351 @default.
- W2801407835 hasRelatedWork W1543558945 @default.
- W2801407835 hasRelatedWork W1967095089 @default.
- W2801407835 hasRelatedWork W1973865997 @default.
- W2801407835 hasRelatedWork W2041141027 @default.
- W2801407835 hasRelatedWork W2049851965 @default.
- W2801407835 hasRelatedWork W2087968352 @default.
- W2801407835 hasRelatedWork W2098586728 @default.
- W2801407835 hasRelatedWork W2152943683 @default.
- W2801407835 hasRelatedWork W2963872103 @default.
- W2801407835 hasRelatedWork W3013620326 @default.
- W2801407835 hasVolume "149" @default.
- W2801407835 isParatext "false" @default.
- W2801407835 isRetracted "false" @default.
- W2801407835 magId "2801407835" @default.
- W2801407835 workType "article" @default.