| Title:
|
Entropy solutions for anisotropic unilateral elliptic problem with Neumann boundary conditions (English) |
| Author:
|
Benboubker, Mohamed Badr |
| Author:
|
Benkhalou, Hayat |
| Author:
|
Hjiaj, Hassane |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0011-4642 |
| ISSN:
|
0862-7959 (print) |
| ISSN:
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2464-7136 (online) |
| Volume:
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151 |
| Issue:
|
2 |
| Year:
|
2026 |
| Pages:
|
169-211 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the following strongly nonlinear Neumann elliptic problem: $$\begin {cases} \displaystyle -\sum ^{N}_{i=1} D^{i} a_{i}(x,u,\nabla u) + H(x,u,\nabla u)+|u|^{p_{0}-2}u = f(x)+\sum ^{N}_{i=1} D^{i} \phi _{i}(x,u) & \mbox {in} \ \Omega ,\\ \displaystyle \sum _{i=1}^{N}(a_{i}(x,u,\nabla u) - \phi _{i}(x,u))\cdot n_{i}= 0 & \mbox {on} \ \partial \Omega , \end {cases}$$ where the Carathéodory functions $a_{i}(x,s,\xi ),$ $H(x,s,\xi )$ and $\phi _{i}(x,s)$ verify some nonstandard conditions. By applying an approximation method, we prove the existence of entropy solutions for the unilateral problem with $L^{1}$-data, and we conclude some regularity results. (English) |
| Keyword:
|
anisotropic Sobolev space |
| Keyword:
|
weak solution |
| Keyword:
|
entropy solution |
| Keyword:
|
strongly nonlinear problem |
| Keyword:
|
Neumann boundary condition |
| Keyword:
|
unilateral problem |
| MSC:
|
35D35 |
| MSC:
|
35J60 |
| DOI:
|
10.21136/MB.2025.0030-24 |
| . |
| Date available:
|
2026-05-19T08:21:02Z |
| Last updated:
|
2026-05-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153618 |
| . |
| Reference:
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