Higher Sobolev and Hölder regularity is studied for local weak solutions of the fractional p-Laplace equation of order s in the case p≥2. Depending on the regime considered, i.e. [Formula presented] precise local estimates are proven. The relevant estimates are stable if the fractional order s reaches 1; the known Sobolev regularity estimates for the local p-Laplace are recovered. The case p=2 reproduces the almost Wloc1+s,2-regularity for the fractional Laplace equation of any order s∈(0,1).
Regularity for the fractional p-Laplace equation
Molica Bisci, Giovanni;
2025-01-01
Abstract
Higher Sobolev and Hölder regularity is studied for local weak solutions of the fractional p-Laplace equation of order s in the case p≥2. Depending on the regime considered, i.e. [Formula presented] precise local estimates are proven. The relevant estimates are stable if the fractional order s reaches 1; the known Sobolev regularity estimates for the local p-Laplace are recovered. The case p=2 reproduces the almost Wloc1+s,2-regularity for the fractional Laplace equation of any order s∈(0,1).File in questo prodotto:
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