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Quasilinear elliptic equations with a source reaction term involving the function and its gradient and measure data

Abstract : We study the equation −div(A(x, u)) = g(x, u, u) + µ where µ is a measure and either g(x, u, u) ∼ |u| q 1 u||u| q 2 or g(x, u, u) ∼ |u| s 1 u + ||u| s 2. We give sufficient conditions for existence of solutions expressed in terms of the Wolff potential or the Riesz potentials of the measure. Finally we connect the potential estimates on the measure with Lipchitz estimates with respect to some Bessel or Riesz capacity.
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https://hal.archives-ouvertes.fr/hal-01775096
Contributor : Laurent Veron <>
Submitted on : Tuesday, March 17, 2020 - 6:16:42 PM
Last modification on : Friday, February 19, 2021 - 4:10:03 PM
Long-term archiving on: : Thursday, June 18, 2020 - 4:22:54 PM

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  • HAL Id : hal-01775096, version 2
  • ARXIV : 1804.09419

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Marie-Françoise Bidaut-Véron, Quoc-Hung Nguyen, Laurent Veron. Quasilinear elliptic equations with a source reaction term involving the function and its gradient and measure data. Calculus of Variations and Partial Differential Equations, Springer Verlag, 2020, 59:148, pp.1-38. ⟨hal-01775096v2⟩

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