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- Title
Multivalued elliptic operators with nonstandard growth.
- Authors
Avci, Mustafa; Pankov, Alexander
- Abstract
The paper is devoted to the Dirichlet problem for monotone, in general multivalued, ellipticequations with nonstandard growth condition. The growth conditions are more general thanthe well-known p ( x ) {p(x)} growth. Moreover, we allow the presence of the so-called Lavrentievphenomenon. As consequence, at least two types of variational settings of Dirichlet problem areavailable. We prove results on the existence of solutions in both of these settings. Then weobtain several results on the convergence of certain types of approximate solutions to an exactsolution.
- Subjects
ELLIPTIC operators; DIRICHLET problem; VARIATIONAL approach (Mathematics); STOCHASTIC convergence; APPROXIMATION theory
- Publication
Advances in Nonlinear Analysis, 2018, Vol 7, Issue 1, p35
- ISSN
2191-9496
- Publication type
Article
- DOI
10.1515/anona-2016-0043