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

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  • Patrizia Di Gironimo

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

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.

Suggested Citation

  • Patrizia Di Gironimo, 2024. "Existence, Regularity, and Uniqueness of Solutions to Some Noncoercive Nonlinear Elliptic Equations in Unbounded Domains," Mathematics, MDPI, vol. 12(12), pages 1-19, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1860-:d:1415042
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    References listed on IDEAS

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    1. Loredana Caso & Patrizia Di Gironimo & Sara Monsurrò & Maria Transirico, 2018. "Uniqueness Results for Higher Order Elliptic Equations in Weighted Sobolev Spaces," International Journal of Differential Equations, Hindawi, vol. 2018, pages 1-6, March.
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