Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 46 min ago
PreprintarXiv licencearXiv

Interior regularity of mixed local-nonlocal parabolic semilinear equations

  • Sergio Junquera
  • Leandro M. Del Pezzo
Open at sourcePDFDOICite

Abstract

In this paper we prove the existence, uniqueness and regularity of classical solutions \break of a semilinear parabolic equation with a mixed local and nonlocal diffusion operator \break ℒ = −(−Δ)s + Δ and Dirichlet boundary conditions. Here, (−Δ)s is the integral fractional laplacian and Δ is the classic local laplacian. We then study the interior regularity of said solutions and conclude that they are Hölder continuous in both space and time, and they are C2,αloc in space for all positive times.

Related

  1. Interior Regularity for Stable Solutions of Semilinear Elliptic Equations with Sign-Changing Nonlinearities
    Long-Han Huang, Yuxuan Zhou, Wenming Zou
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Liouville Theorems for Semilinear Parabolic Equations Involving the Nonlinear Gradient Term
    Xue Li
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Global Hölder solvability for parabolic equations with interior Morrey data
    Takanobu Hara
    arXivPreprintarXiv licenceFull textAnalysis & PDEsProbabilityarXiv
  4. Concentration of measure-valued solutions for semilinear parabolic equations
    Charlie Lebarbé, Émilien Flayac, Michel Fournié +2
    HALPreprintCC BY 4.0Full textOptimisation & controlHAL
  5. An eps-regularity criterion at one scale for 3-D Navier-Stokes equations and improved upper bound on the box dimension of the interior singular set
    Yi Lu, Rongrong Chi, Wei Ren
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{junquera2026interior,
  title = {{Interior regularity of mixed local-nonlocal parabolic semilinear equations}},
  author = {Sergio Junquera and Leandro M. Del Pezzo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06537},
  eprint = {2610.06537},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06537},
}
RIS
TY  - UNPB
TI  - Interior regularity of mixed local-nonlocal parabolic semilinear equations
AU  - Sergio Junquera
AU  - Leandro M. Del Pezzo
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.06537
UR  - https://arxiv.org/abs/2610.06537
AB  - In this paper we prove the existence, uniqueness and regularity of classical solutions \break of a semilinear parabolic equation with a mixed local and nonlocal diffusion operator \break ℒ = −(−Δ)^s + Δ and Dirichlet boundary conditions. Here, (−Δ)^s is the integral fractional laplacian and Δ is the classic local laplacian. We then study the interior regularity of said solutions and conclude that they are Hölder continuous in both space and time, and they are C^2,α_loc in space for all positive times.
ER  -