Existence, Regularity, and Uniqueness of Solutions to Some Noncoercive Nonlinear Elliptic Equations in Unbounded Domains

Patrizia Di Gironimo ()
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Patrizia Di Gironimo: Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 84084 Fisciano, Italy

Mathematics, 2024, vol. 12, issue 12, 1-19

Abstract: In this paper, we study a noncoercive nonlinear elliptic operator with a drift term in an unbounded domain. The singular first-order term grows like | E ( x ) | | ∇ u | , where E ( x ) is a vector field belonging to a suitable Morrey-type space. Our operator arises as a stationary equation of diffusion–advection problems. We prove existence, regularity, and uniqueness theorems for a Dirichlet problem. To obtain our main results, we use the weak maximum principle and the same a priori estimates.

Keywords: noncoercive nonlinear elliptic equations; Dirichlet problems; singular drift; unbounded domains (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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