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Nonlinear elliptic equations with measure valued absorption potential
Abstract : We study the semilinear elliptic equation −∆u + g(u)σ = µ with Dirichlet boundary condition in a smooth bounded domain where σ is a nonnegative Radon measure, µ a Radon measure and g is an absorbing nonlinearity. We show that the problem is well posed if we assume that σ belongs to some Morrey class. Under this condition we give a general existence result for any bounded measure provided g satisfies a subcritical integral assumption. We study also the supercritical case when g(r) = |r| ^{q−1} r, with q > 1 and µ satisfies an absolute continuity condition expressed in terms of some capacities involving σ. 2010 Mathematics Subject Classification. 35 J 61; 31 B 15; 28 C 05 .
Cited literature [25 references]
https://hal.archives-ouvertes.fr/hal-01726015
Contributor : Laurent Veron Connect in order to contact the contributor
Submitted on : Wednesday, March 7, 2018 - 5:17:37 PM
Last modification on : Friday, April 1, 2022 - 3:56:49 AM
Long-term archiving on: : Friday, June 8, 2018 - 3:10:36 PM
Contributor : Laurent Veron Connect in order to contact the contributor
Submitted on : Wednesday, March 7, 2018 - 5:17:37 PM
Last modification on : Friday, April 1, 2022 - 3:56:49 AM
Long-term archiving on: : Friday, June 8, 2018 - 3:10:36 PM
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