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On the behaviour of the solutions to p-Laplacian equations as p goes to 1
Mercaldo, A.
Segura de León, S.
Trombetti, C.

Data: 2008
Resum: In the present paper we study the behaviour as SpS goes to S1S of the weak solutions to the problemsSS\begin{cases}-\operatorname{div} \bigl( $\ nabla u_p $^ {p-2}\nabla u_p\bigr)=f&\text{in } \Omega\\u_p=0 &\text{on } \partial\Omega,\end{cases}SSwhere S\OmegaS is a bounded open set of S{\mathbb R}^NS S(N\ge 2)S with Lipschitz boundary and Sp > 1S. As far as the datum SfS is concerned, we analyze several cases: the most general one is Sf\in W^{-1,\infty}(\Omega)S. We also illustrate our results by means of remarks and examples.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 52 n. 2 (2008) p. 377-411, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_52208_07

35 p, 299.4 KB

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