Hölder regularity for the fractional p-Laplacian, revisited
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Filippo Maria Cassanello
Abstract
We present an alternative proof for local Hölder regularity of the solutions of the fractional p-Laplace equations, based on clustering and expansion (more precisely, recentering) of positivity.
Funding statement: The authors are members of GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica ’Francesco Severi’). Antonio Iannizzotto is partially supported by the research project Problemi non locali di tipo stazionario ed evolutivo (GNAMPA, CUP E53C23001670001).
Acknowledgements
We would like to thank the anonymous Referees for their useful comments.
References
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© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- A characterization of ℓ1 double bubbles with general interface interaction
- The weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth
- On the behavior in time of the solutions to total variation flow
- Zaremba problem with degenerate weights
- Point-wise characterizations of limits of planar Sobolev homeomorphisms and their quasi-monotonicity
- Struwe’s global compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group
- On the variational nature of the Anzellotti pairing
- Strongly nonlinear Robin problems for harmonic and polyharmonic functions in the half-space
- Upper semicontinuity of index plus nullity for minimal and CMC hypersurfaces
- A variational approach to the Navier–Stokes equations with shear-dependent viscosity
- Hölder regularity for the fractional p-Laplacian, revisited
- Poincaré inequality and energy of separating sets
- On a class of obstacle problems with (p, q)-growth and explicit u-dependence
- Stepanov differentiability theorem for intrinsic graphs in Heisenberg groups
- Parabolic Lipschitz truncation for multi-phase problems: The degenerate case
Artikel in diesem Heft
- Frontmatter
- A characterization of ℓ1 double bubbles with general interface interaction
- The weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth
- On the behavior in time of the solutions to total variation flow
- Zaremba problem with degenerate weights
- Point-wise characterizations of limits of planar Sobolev homeomorphisms and their quasi-monotonicity
- Struwe’s global compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group
- On the variational nature of the Anzellotti pairing
- Strongly nonlinear Robin problems for harmonic and polyharmonic functions in the half-space
- Upper semicontinuity of index plus nullity for minimal and CMC hypersurfaces
- A variational approach to the Navier–Stokes equations with shear-dependent viscosity
- Hölder regularity for the fractional p-Laplacian, revisited
- Poincaré inequality and energy of separating sets
- On a class of obstacle problems with (p, q)-growth and explicit u-dependence
- Stepanov differentiability theorem for intrinsic graphs in Heisenberg groups
- Parabolic Lipschitz truncation for multi-phase problems: The degenerate case
