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Article Dans Une Revue Calculus of Variations and Partial Differential Equations Année : 2020

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

Résumé

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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Dates et versions

hal-01775096 , version 1 (24-04-2018)
hal-01775096 , version 2 (17-03-2020)

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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, 2020, 59:148, pp.1-38. ⟨10.1007/s00526-020-01808-3⟩. ⟨hal-01775096v2⟩
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