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Global Hölder regularity for the fractional \(p\)-Laplacian. (English) Zbl 1433.35447
Summary: By virtue of barrier arguments we prove \(C^\alpha\)-regularity up to the boundary for the weak solutions of a non-local, non-linear 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.

MSC:
35R11 Fractional partial differential equations
35B65 Smoothness and regularity of solutions to PDEs
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
47G20 Integro-differential operators
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