Global Hölder regularity for the fractional $p$-Laplacian
نویسندگان
چکیده
منابع مشابه
Global Regularity for the Free Boundary in the Obstacle Problem for the Fractional Laplacian
We study the regularity of the free boundary in the obstacle problem for the fractional Laplacian under the assumption that the obstacle φ satisfies ∆φ ≤ 0 near the contact region. Our main result establishes that the free boundary consists of a set of regular points, which is known to be a (n− 1)-dimensional C manifold by the results in [7], and a set of singular points, which we prove to be c...
متن کاملRegularity for the Supercritical Fractional Laplacian with Drift
We consider the linear stationary equation defined by the fractional Laplacian with drift. In the supercritical case, wherein the dominant term is given by the drift instead of the diffusion component, we prove local regularity of solutions in Sobolev spaces employing tools from the theory of pseudo-differential operators. The regularity of solutions in the supercritical case is as expected fro...
متن کاملDirectional Hölder Metric Regularity
This paper sheds new light on regularity of multifunctions through various characterizations of directional Hölder/Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional Hölder/Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directi...
متن کاملTHE BREZIS-NIRENBERG PROBLEM FOR THE FRACTIONAL p-LAPLACIAN
We obtain nontrivial solutions to the Brezis-Nirenberg problem for the fractional p-Laplacian operator, extending some results in the literature for the fractional Laplacian. The quasilinear case presents two serious new difficulties. First an explicit formula for a minimizer in the fractional Sobolev inequality is not available when p 6= 2. We get around this difficulty by working with certain...
متن کاملStability of variational eigenvalues for the fractional p–Laplacian
By virtue of Γ−convergence arguments, we investigate the stability of variational eigenvalues associated with a given topological index for the fractional p−Laplacian operator, in the singular limit as the nonlocal operator converges to the p−Laplacian. We also obtain the convergence of the corresponding normalized eigenfunctions in a suitable fractional norm.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 2016
ISSN: 0213-2230
DOI: 10.4171/rmi/921