Journal article
Nonlinear gradient estimates for elliptic equations in quasiconvex domains
Calculus of variations and partial differential equations, Vol.54(2), pp.1425-1453
10/2015
DOI: 10.1007/s00526-015-0830-5
Abstract
We study a general model of nonvariational elliptic equations of \(p\)-Laplacian type in quasiconvex domains, which are locally approximated by convex domains. We prove that both the gradient and the associated nonhomogeneous term belong to the same \(L^q\) space for every \(q \in [p, \infty )\). As far as the domain is concerned, our regularity assumption on the boundary is weaker than any other one reported in this direction. In addition, we extend our result in Lebesgue spaces to Orlicz spaces.
Details
- Title: Subtitle
- Nonlinear gradient estimates for elliptic equations in quasiconvex domains
- Creators
- Sun-Sig Byun - Department of Mathematical Science Seoul National University Seoul 151-747 Republic of KoreaHun Kwon - Department of Mathematical Science Seoul National University Seoul 151-747 Republic of KoreaHyoungsuk So - Department of Mathematical Science Seoul National University Seoul 151-747 Republic of KoreaLihe Wang - University of Iowa, Mathematics
- Resource Type
- Journal article
- Publication Details
- Calculus of variations and partial differential equations, Vol.54(2), pp.1425-1453
- Publisher
- Springer Berlin Heidelberg
- DOI
- 10.1007/s00526-015-0830-5
- ISSN
- 0944-2669
- eISSN
- 1432-0835
- Language
- English
- Date published
- 10/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9984083804302771
Metrics
6 Record Views