| Full text | |
| Author(s): |
Fiscella, Alessio
Total Authors: 1
|
| Document type: | Journal article |
| Source: | APPLIED MATHEMATICS AND OPTIMIZATION; v. 85, n. 3, p. 16-pg., 2022-05-10. |
| Abstract | |
In this paper, we deal with the following double phase problem {- div (vertical bar del u vertical bar(p-2) del u + a (x) vertical bar del u vertical bar(q-2) del u) = gamma + f (x, u) (vertical bar u vertical bar(p-2)u/vertical bar x vertical bar(p) + a(x) vertical bar u vertical bar(q-2) u/vertical bar x vertical bar(q)) in Omega, u = 0 in partial derivative partial derivative Omega, where Omega subset of R-N is an open, bounded set with Lipschitz boundary, 0 is an element of Omega, N >= 2, 1 < p < q < N, weight a(.) >= 0, gamma is areal parameter and f is a subcritical function. By variational method, we provide the existence of a non-trivial weak solution on the Musielak-Orlicz-Sobolev space W-0(1,H) (Omega), with modular functionH(t, x) = t(p) + a(x)t(q). For this, we first introduce the Hardy inequalities for space W-0(1,H) (Omega), under suitable assumptions on a(.). (AU) | |
| FAPESP's process: | 19/23917-3 - Operator with non standard growth |
| Grantee: | Alessio Fiscella |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 19/02512-5 - Systems and partial differential equations |
| Grantee: | Marcelo da Silva Montenegro |
| Support Opportunities: | Research Projects - Thematic Grants |