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.
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Boccardo, L., Croce, G. & Orsina, L. Nonlinear degenerate elliptic problems with \({{W^{1,1}_{0}(\Omega)}}\) solutions. manuscripta math. 137, 419–439 (2012). https://doi.org/10.1007/s00229-011-0473-6
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DOI: https://doi.org/10.1007/s00229-011-0473-6