Local regularity results for solutions of linear elliptic equations with drift term

G. R. Cirmi; S. D’Asero; Salvatore Leonardi; Michaela M. Porzio

doi:10.1515/acv-2019-0048

Article

Local regularity results for solutions of linear elliptic equations with drift term

G. R. Cirmi , S. D’Asero , Salvatore Leonardi and Michaela M. Porzio

Published/Copyright: November 20, 2019

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From the journal Advances in Calculus of Variations Volume 15 Issue 1

Abstract

We study the local regularity of the solution u of the following nonlinear boundary value problem:

{ 𝒜 ⁢ u = - div ⁡ [ E ⁢ ( x ) ⁢ u + F ⁢ ( x ) ] in ⁢ Ω , u = 0 on ⁢ ∂ ⁡ Ω ,

where Ω is a bounded open subset of ℝ N , with N > 2 , 𝒜 is a nonlinear Leray–Lions operator in divergence form, and E ⁢ ( x ) and F ⁢ ( x ) are vector fields satisfying suitable local summability properties.

Keywords: Drift term; local regularity; elliptic equation

MSC 2010: 35J25; 35B65

Communicated by Jan Bruinier

Funding statement: The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). This paper was supported by FIR 2018 and Piano Triennale della Ricerca 2016-2018 (UNICT).

Acknowledgements

The authors are indebted to the anonymous reviewer who contributed to improve the original manuscript with helpful suggestions.

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Received: 2019-05-14

Revised: 2019-10-08

Accepted: 2019-10-25

Published Online: 2019-11-20

Published in Print: 2022-01-01

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https://doi.org/10.1515/acv-2019-0048

Keywords for this article

Drift term; local regularity; elliptic equation