Dirichlet problem for noncoercive nonlinear elliptic equations with singular drift term in unbounded domains
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS(2023)
Abstract
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.
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Key words
Noncoercive nonlinear elliptic equations,singular drift,Dirichlet problems,unbounded domains
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