We investigate the obstacle problem for a class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p-Laplacian operator with measurable coefficients. Amongst other results, we will prove both the existence and uniqueness of the solutions to the obstacle problem, and that these solutions inherit regularity properties, such as boundedness, continuity and Hölder continuity (up to the boundary), from the obstacle.

The obstacle problem for nonlinear integro-differential operators / Korvenpää, Janne; Kuusi, Tuomo; Palatucci, Giampiero. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 55:3(2016), pp. 1-30. [10.1007/s00526-016-0999-2]

The obstacle problem for nonlinear integro-differential operators

PALATUCCI, Giampiero
2016

Abstract

We investigate the obstacle problem for a class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p-Laplacian operator with measurable coefficients. Amongst other results, we will prove both the existence and uniqueness of the solutions to the obstacle problem, and that these solutions inherit regularity properties, such as boundedness, continuity and Hölder continuity (up to the boundary), from the obstacle.
The obstacle problem for nonlinear integro-differential operators / Korvenpää, Janne; Kuusi, Tuomo; Palatucci, Giampiero. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 55:3(2016), pp. 1-30. [10.1007/s00526-016-0999-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2815070
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