Affiliation:
1. Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain
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 L N ( 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 H 0 1 ( 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.
Reference16 articles.
1. An L 1 theory of existence and uniqueness of solutions of nonlinear elliptic equations;Bénilan;Ann. Scuola Norm. Sup. Pisa, Serie IV,1995
2. Dirichlet problems with singular convection terms and applications;Boccardo;J. Differential Equations,2015
3. L. Boccardo, Stampacchia–Calderón–Zygmund theory for linear elliptic equations with discontinuous coefficients and singular drift, ESAIM Control Optim. Calc. Var. 25 (2019), 47, 13 pp.
4. L. Boccardo, Weak maximum principle for Dirichlet problems with convection or drift terms, Math. Eng. 3 (2021), 026, 9 pp.
5. The impact of the zero order term in the study of Dirichlet problems with convection or drift terms;Boccardo;Rev. Mat. Complut.,2023