An elliptic problem in dimension N with a varying drift term bounded in LN

Article type: Research Article

Authors: Casado-Díaz, Juan^{; *}

Affiliations: Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain

Correspondence: [*] Corresponding author. E-mail: jcasadod@us.es.

Abstract: The present paper is devoted to study the asymptotic behavior of a sequence of linear elliptic equations with a varying drift term, whose coefficients are just bounded in LN(Ω), with N the dimension of the space. It is known that there exists a unique solution for each of these problems in the Sobolev space H01(Ω). However, because the operators are not coercive, there is no uniform estimate of the solutions in this space. We use some estimates in (J. Differential Equations 258 (2015) 2290–2314), and a regularization obtained by adding a small nonlinear first order term, to pass to the limit in these problems.

Keywords: Asymptotic behavior, elliptic problem, drift term, varying coefficients

DOI: 10.3233/ASY-241914

Journal: Asymptotic Analysis, vol. 140, no. 3-4, pp. 147-158, 2024