In the present paper we study the behaviour, as p goes to 1, of the renormalized solutions to the Dirichlet problems for the p-laplacian equations with summable datum. We prove that these renormalized solutions pointwise converge, up to ``subsequences", to a function which is a solution to a ``limit problem" involving the so called 1-Laplace operator.
On the solutions to 1-Laplacian equation with L^1 data / Mercaldo, Anna; S., Segura de Leon; Trombetti, Cristina. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 256:8(2009), pp. 2387-2416. [10.1016/j.jfa.2008.12.025]
On the solutions to 1-Laplacian equation with L^1 data
MERCALDO, ANNA;TROMBETTI, CRISTINA
2009
Abstract
In the present paper we study the behaviour, as p goes to 1, of the renormalized solutions to the Dirichlet problems for the p-laplacian equations with summable datum. We prove that these renormalized solutions pointwise converge, up to ``subsequences", to a function which is a solution to a ``limit problem" involving the so called 1-Laplace operator.File in questo prodotto:
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