We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a unique W 0 1,1(Ω) 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. © 2011 Springer-Verlag.
Nonlinear degenerate elliptic problems with W 0 1,1(Ω) solutions / Boccardo, Lucio; Gisella, Croce; Orsina, Luigi. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - STAMPA. - 137:3(2012), pp. 419-439. [10.1007/s00229-011-0473-6]
Nonlinear degenerate elliptic problems with W 0 1,1(Ω) solutions
BOCCARDO, Lucio;ORSINA, Luigi
2012
Abstract
We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a unique W 0 1,1(Ω) 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. © 2011 Springer-Verlag.File allegati a questo prodotto
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