In this note, we will study the problem (Equation Presented), where 0 < s < 1, (-δ)sp is the nonlocal p-Laplacian defined below, Ω is a smooth bounded domain. The main point studied in this work is to prove, adapting the techniques used in [31] for the case p = 2 to the general case p ∈ (1, + ∞), the summability of the finite energy solutions in terms of the summability of a source term f(Χ). The aim of this note is to present the results in a way as elementary as possible.
Barrios, B., Peral, I., Vita, S. (2015). Some remarks about the summability of nonlocal nonlinear problems. ADVANCES IN NONLINEAR ANALYSIS, 4(2), 91-107 [10.1515/anona-2015-0012].
Some remarks about the summability of nonlocal nonlinear problems
Vita, S
2015
Abstract
In this note, we will study the problem (Equation Presented), where 0 < s < 1, (-δ)sp is the nonlocal p-Laplacian defined below, Ω is a smooth bounded domain. The main point studied in this work is to prove, adapting the techniques used in [31] for the case p = 2 to the general case p ∈ (1, + ∞), the summability of the finite energy solutions in terms of the summability of a source term f(Χ). The aim of this note is to present the results in a way as elementary as possible.
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