Matches in SemOpenAlex for { <https://semopenalex.org/work/W4310999541> ?p ?o ?g. }
Showing items 1 to 68 of
68
with 100 items per page.
- W4310999541 abstract "We present an extension of the classical De Giorgi class, and then we show that functions in this new class are locally bounded and locally Holder continuous. Some applications are given. As a first application, we give a regularity result for local minimizers $u:Omega subset mathbb R^4 rightarrow mathbb R^4$ of a special class of polyconvex functionals with splitting form in four dimensional Euclidean spaces. Under some structural conditions on the energy density, we prove that each component $u^alpha$ of the local minimizer $u$ belongs to the generalized De Giorgi class, then one can derive that it is locally bounded and locally Holder continuous. Our result can be applied to polyconvex integrals whose prototype is $$ int_Omega Big(sum_{alpha =1}^4 |Du^alpha|^p + sum_{beta =1}^6 |({rm adj}_2 Du )^beta | ^q +sum_{gamma =1}^4 |({rm adj}_3 Du )^gamma | ^r +|det Du|^s Big ) mathrm {d}x $$ with suitable $p,q,r,sge 1$. As a second application, we consider a degenerate linear elliptic equation of the form $$ -mbox {div} (a(x)nabla u)=-mbox {div}F, $$ with $0<a(x) le beta <+infty$. We prove, by virtue of the generalized De Giorgi class, that any weak solution is locally bounded and locally Holder continuous provided that $frac 1 {a(x)}$ and $F(x)$ belong to some suitable locally integrable function spaces. As a third application, we show that our theorem can be applied in dealing with regularity issues of elliptic equations with non-standard grow conditions. As a fourth application we treat with quasilinear elliptic systems. Under suitable assumptions on the coefficients, we show that any of its weak solutions is locally bounded and locally Holder continuous." @default.
- W4310999541 created "2022-12-22" @default.
- W4310999541 creator A5061837724 @default.
- W4310999541 creator A5062253236 @default.
- W4310999541 creator A5084746751 @default.
- W4310999541 date "2022-12-08" @default.
- W4310999541 modified "2023-10-17" @default.
- W4310999541 title "An Extension of De Giorgi Class and Applications" @default.
- W4310999541 doi "https://doi.org/10.48550/arxiv.2212.04170" @default.
- W4310999541 hasPublicationYear "2022" @default.
- W4310999541 type Work @default.
- W4310999541 citedByCount "0" @default.
- W4310999541 crossrefType "posted-content" @default.
- W4310999541 hasAuthorship W4310999541A5061837724 @default.
- W4310999541 hasAuthorship W4310999541A5062253236 @default.
- W4310999541 hasAuthorship W4310999541A5084746751 @default.
- W4310999541 hasBestOaLocation W43109995411 @default.
- W4310999541 hasConcept C114614502 @default.
- W4310999541 hasConcept C121332964 @default.
- W4310999541 hasConcept C134306372 @default.
- W4310999541 hasConcept C154945302 @default.
- W4310999541 hasConcept C199360897 @default.
- W4310999541 hasConcept C200741047 @default.
- W4310999541 hasConcept C202444582 @default.
- W4310999541 hasConcept C2777212361 @default.
- W4310999541 hasConcept C2778029271 @default.
- W4310999541 hasConcept C2779557605 @default.
- W4310999541 hasConcept C33923547 @default.
- W4310999541 hasConcept C34388435 @default.
- W4310999541 hasConcept C41008148 @default.
- W4310999541 hasConcept C54207081 @default.
- W4310999541 hasConcept C62520636 @default.
- W4310999541 hasConcept C72319582 @default.
- W4310999541 hasConcept C83295520 @default.
- W4310999541 hasConceptScore W4310999541C114614502 @default.
- W4310999541 hasConceptScore W4310999541C121332964 @default.
- W4310999541 hasConceptScore W4310999541C134306372 @default.
- W4310999541 hasConceptScore W4310999541C154945302 @default.
- W4310999541 hasConceptScore W4310999541C199360897 @default.
- W4310999541 hasConceptScore W4310999541C200741047 @default.
- W4310999541 hasConceptScore W4310999541C202444582 @default.
- W4310999541 hasConceptScore W4310999541C2777212361 @default.
- W4310999541 hasConceptScore W4310999541C2778029271 @default.
- W4310999541 hasConceptScore W4310999541C2779557605 @default.
- W4310999541 hasConceptScore W4310999541C33923547 @default.
- W4310999541 hasConceptScore W4310999541C34388435 @default.
- W4310999541 hasConceptScore W4310999541C41008148 @default.
- W4310999541 hasConceptScore W4310999541C54207081 @default.
- W4310999541 hasConceptScore W4310999541C62520636 @default.
- W4310999541 hasConceptScore W4310999541C72319582 @default.
- W4310999541 hasConceptScore W4310999541C83295520 @default.
- W4310999541 hasLocation W43109995411 @default.
- W4310999541 hasLocation W43109995412 @default.
- W4310999541 hasOpenAccess W4310999541 @default.
- W4310999541 hasPrimaryLocation W43109995411 @default.
- W4310999541 hasRelatedWork W1539596337 @default.
- W4310999541 hasRelatedWork W1855007440 @default.
- W4310999541 hasRelatedWork W2229925025 @default.
- W4310999541 hasRelatedWork W2788247819 @default.
- W4310999541 hasRelatedWork W2792440356 @default.
- W4310999541 hasRelatedWork W3096849461 @default.
- W4310999541 hasRelatedWork W3112745479 @default.
- W4310999541 hasRelatedWork W33469805 @default.
- W4310999541 hasRelatedWork W4298128264 @default.
- W4310999541 hasRelatedWork W4378474062 @default.
- W4310999541 isParatext "false" @default.
- W4310999541 isRetracted "false" @default.
- W4310999541 workType "article" @default.