The obstacle problem for nonlinear integro-differential operators
By Janne Korvenpää, Tuomo Kuusi, Giampiero Palatucci. Calculus of Variations and Partial Differential Equations, 2016
107 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/44d4e5103b33a965739491911d8cd51318c4f16b
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In Applied Mathematics
- Cristiana De Filippis
- Giuseppe Mingione
- Jihoon Ok
- Giampiero Palatucci
- Lorenzo Brasco
- Sun-Sig Byun
- Erik Lindgren
- Kyeong Song
In Computational Theory and Mathematics
- Cristiana De Filippis
- Giuseppe Mingione
- Giampiero Palatucci
- Jihoon Ok
- Lorenzo Brasco
- Erik Lindgren
- Sun-Sig Byun
- Kyeong Song
In Mathematical Physics
- Cristiana De Filippis
- Lorenzo Brasco
- Jihoon Ok
- Erik Lindgren
- Sun-Sig Byun
- Giampiero Palatucci
- Kyeong Song
- Giuseppe Mingione
Citations in the corpus
- Hölder regularity for weak solutions to nonlocal double phase problems (2021, background): “Such approaches are further applied to several research areas including obstacle problems [29] and measure data problems [30].”
- Continuity of solutions to a nonlinear fractional diffusion equation (2019, background): “The regularity of solutions has been studied for instance in [3, 4, 6, 12, 13, 17, 16, 19, 20, 21, 24, 27] and [34].”
- Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations (2016, unknown): “2 Some recent results on nonlocal fractional operators In this section, we recall some recent results for fractional weak sub- and supersolutions, which we adapted to our framework for the sake of the reader; see [9, 10, 20] for the related proofs.”
- Hölder regularity for nonlocal double phase equations (2019, background): “We refer also to Section 2 in [22] where similar inequalities do appear.”