A Dirichlet problem involving the divergence operator

G. Csató; B. Dacorogna

doi:10.1016/j.anihpc.2015.01.006

JournalsaihpcVol. 33, No. 3pp. 829–848

A Dirichlet problem involving the divergence operator

G. Csató
Tata Institute of Fundamental Research, Centre for Applicable Mathematics, 560065 Bangalore, India
B. Dacorogna
Section de Mathématiques, EPFL, 1015 Lausanne, Switzerland

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Abstract

We consider the problem

{div u + ⟨ a; u ⟩ = f u = u_{0} in Ω on \partial Ω.

We show that if $curl a (x_{0}) \neq = 0$ for some $x_{0} \in Ω$ , then the problem is solvable without restriction on $f$ . We also discuss the regularity of the solution.

Cite this article

G. Csató, B. Dacorogna, A Dirichlet problem involving the divergence operator. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 3, pp. 829–848

DOI 10.1016/J.ANIHPC.2015.01.006