Manuscripta Mathematica

, Volume 137, Issue 3–4, pp 419–439 | Cite as

Nonlinear degenerate elliptic problems with \({{W^{1,1}_{0}(\Omega)}}\) solutions

Article

Abstract

We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a unique \({{W^{1,1}_{0}(\Omega)}}\) distributional solution under suitable summability assumptions on the source in Lebesgue spaces. Moreover, we prove that our problem has no solution if the source is a Radon measure concentrated on a set of zero harmonic capacity.

Mathematics Subject Classification (2010)

35D30 35J65 35J70 

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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Dipartimento di Matematica“Sapienza” Università di RomaRomaItaly
  2. 2.Laboratoire de Mathématiques Appliquées du HavreUniversité du HavreLe HavreFrance

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