Global H\"older regularity for the fractional $p$-Laplacian

Antonio Iannizzotto; Sunra Mosconi; Marco Squassina

Global H\"older regularity for the fractional $p$-Laplacian

Analysis of PDEs 2015-10-28 v2

Authors: Antonio Iannizzotto , Sunra Mosconi , Marco Squassina

Abstract

By virtue of barrier arguments we prove $C^\alpha$ -regularity up to the boundary for the weak solutions of a non-local nonlinear problem driven by the fractional $p$ -Laplacian operator. The equation is boundedly inhomogeneous and the boundary conditions are of Dirichlet type. We employ different methods according to the singular ( $p<2$ ) of degenerate ( $p>2$ ) case.

Keywords

fractional p-Laplacian global H\"older regularity non-local nonlinear problems weak solutions barrier arguments Dirichlet boundary conditions singular case degenerate case

Cite

@article{arxiv.1411.2956,
  title  = {Global H\"older regularity for the fractional $p$-Laplacian},
  author = {Antonio Iannizzotto and Sunra Mosconi and Marco Squassina},
  journal= {arXiv preprint arXiv:1411.2956},
  year   = {2015}
}

Comments

41 pages, Rev. Mat. Iberoam., to appear

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