Multivalued elliptic operators with nonstandard growth
The paper is devoted to the Dirichlet problem for monotone, in general multivalued, elliptic equations with nonstandard growth condition. The growth conditions are more general than the well-known p(x){p(x)} growth. Moreover, we allow the presence of the so-called Lavrentiev phenomenon. As conseque...
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doaj-87d677e9e2c349c3a773a3eb0dc66b262021-09-06T19:39:54ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2018-02-0171354810.1515/anona-2016-0043Multivalued elliptic operators with nonstandard growthAvci Mustafa0Pankov Alexander1Faculty of Economics and Administrative Sciences, Batman University, Batman, TurkeyMathematics Department, Morgan State University, Baltimore, USAThe paper is devoted to the Dirichlet problem for monotone, in general multivalued, elliptic equations with nonstandard growth condition. The growth conditions are more general than the well-known p(x){p(x)} growth. Moreover, we allow the presence of the so-called Lavrentiev phenomenon. As consequence, at least two types of variational settings of Dirichlet problem are available. We prove results on the existence of solutions in both of these settings. Then we obtain several results on the convergence of certain types of approximate solutions to an exact solution.https://doi.org/10.1515/anona-2016-0043nonstandard growth conditionmonotone elliptic equationmultivalued monotone operator35j60 35j25 35r70 47h05 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Avci Mustafa Pankov Alexander |
spellingShingle |
Avci Mustafa Pankov Alexander Multivalued elliptic operators with nonstandard growth Advances in Nonlinear Analysis nonstandard growth condition monotone elliptic equation multivalued monotone operator 35j60 35j25 35r70 47h05 |
author_facet |
Avci Mustafa Pankov Alexander |
author_sort |
Avci Mustafa |
title |
Multivalued elliptic operators with nonstandard growth |
title_short |
Multivalued elliptic operators with nonstandard growth |
title_full |
Multivalued elliptic operators with nonstandard growth |
title_fullStr |
Multivalued elliptic operators with nonstandard growth |
title_full_unstemmed |
Multivalued elliptic operators with nonstandard growth |
title_sort |
multivalued elliptic operators with nonstandard growth |
publisher |
De Gruyter |
series |
Advances in Nonlinear Analysis |
issn |
2191-9496 2191-950X |
publishDate |
2018-02-01 |
description |
The paper is devoted to the Dirichlet problem for monotone, in general multivalued, elliptic
equations with nonstandard growth condition. The growth conditions are more general than
the well-known p(x){p(x)} growth. Moreover, we allow the presence of the so-called Lavrentiev
phenomenon. As consequence, at least two types of variational settings of Dirichlet problem are
available. We prove results on the existence of solutions in both of these settings. Then we
obtain several results on the convergence of certain types of approximate solutions to an exact
solution. |
topic |
nonstandard growth condition monotone elliptic equation multivalued monotone operator 35j60 35j25 35r70 47h05 |
url |
https://doi.org/10.1515/anona-2016-0043 |
work_keys_str_mv |
AT avcimustafa multivaluedellipticoperatorswithnonstandardgrowth AT pankovalexander multivaluedellipticoperatorswithnonstandardgrowth |
_version_ |
1717769801937453056 |