Remarks on nonlinear equations with measures

2011/02/28 by Moshe Marcus, Marcus, Moshe
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1102.5692

10 pages

arxiv created 2011/02/28 · arxiv updated 2011/03/01

Abstract

We study the Dirichlet boundary value problem for equations with absorption of the form -Δu+g∘ u=μ in a bounded domain Ω⊂ R^N where g is a continuous odd monotone increasing function. Under some additional assumptions on g, we present necessary and sufficient conditions for existence when μ is a finite measure. We also discuss the notion of solution when the measure μ is positive and blows up on a compact subset of \Gw.

Related

• Nonlinear elliptic equations with measure valued absorption potential
• Measure data problems for a class of elliptic equations with mixed\n absorption-reaction
• Diffuse measures and nonlinear parabolic equations
• Generalized solutions to semilinear elliptic equations with measure data
• Elliptic equations with nonlinear absorption depending on the solution and its gradient