| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 85 | |
| Number of page(s) | 24 | |
| DOI | https://doi.org/10.1051/cocv/2023076 | |
| Published online | 27 November 2023 | |
Dirichlet problem for noncoercive nonlinear elliptic equations with singular drift term in unbounded domains
1
Dipartimento di Matematica Università degli Studi di Salerno Via Giovanni Paolo II, 84084 Fisciano (SA), Italy
2
Dipartimento di Matematica e Applicazioni “R. Caccioppoli” Università degli Studi di Napoli Federico II Via Cintia, 80126 Napoli, Italy
* Corresponding author: smonsurro@unisa.it
Received:
29
November
2022
Accepted:
22
October
2023
In this paper, we study a Dirichlet problem for noncoercive nonlinear elliptic equations with first order term in an unbounded domain. We obtain Stampacchia type existence, regularity and uniqueness results, when the singular drift term is controlled through a function in a suitable functional space, strictly containing Lebesgue one. The main tools are a weak maximum principle together with some a priori estimates proved by contradiction.
Mathematics Subject Classification: 35A15 / 35J25 / 35B65
Key words: Noncoercive nonlinear elliptic equations / singular drift / Dirichlet problems / unbounded domains
© The authors. Published by EDP Sciences, SMAI 2023
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