6533b821fe1ef96bd127c491
RESEARCH PRODUCT
On the solutions to 1-Laplacian equation with L1 data
Sergio Segura De LeónCristina TrombettiAnna Mercaldosubject
Discrete mathematicsPointwise1-Laplace operatorRenormalized solutionsOpen setBoundary (topology)Function (mathematics)Nonlinear elliptic equationsLipschitz continuityRenormalized solutionBounded functionSummable dataLimit (mathematics)L1-data1Laplce operatorLaplace operatorAnalysisMathematicsdescription
AbstractIn the present paper we study the behaviour, as p goes to 1, of the renormalized solutions to the problems(0.1){−div(|∇up|p−2∇up)=finΩ,up=0on∂Ω, where p>1, Ω is a bounded open set of RN (N⩾2) with Lipschitz boundary and f belongs to L1(Ω). We prove that these renormalized solutions pointwise converge, up to “subsequences,” to a function u. With a suitable definition of solution we also prove that u is a solution to a “limit problem.” Moreover we analyze the situation occurring when more regular data f are considered.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-04-01 | Journal of Functional Analysis |