Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772201 | Journal of Functional Analysis | 2017 | 76 Pages |
Abstract
We study energy functionals obtained by adding a possibly discontinuous potential to an interaction term modeled upon a Gagliardo-type fractional seminorm. We prove that minimizers of such non-differentiable functionals are locally bounded, Hölder continuous, and that they satisfy a suitable Harnack inequality. Hence, we provide an extension of celebrated results of M. Giaquinta and E. Giusti to the nonlocal setting. To do this, we introduce a particular class of fractional Sobolev functions, reminiscent of that considered by E. De Giorgi in his seminal paper of 1957. The flexibility of these classes allows us to also establish regularity of solutions to rather general nonlinear integral equations.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Matteo Cozzi,