Local regularity of very weak -harmonic functions via fractional difference quotients

  • Alessandro Carbotti

    Università del Salento, Lecce, Italy
  • Simone Cito

    Università del Salento, Lecce, Italy
  • Domenico Angelo La Manna

    Università degli studi di Napoli “Federico II”, Naples, Italy
  • Diego Pallara

    Università del Salento, and INFN, Sezione di Lecce, Lecce, Italy
Local regularity of very weak $s$-harmonic functions via fractional difference quotients cover
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Abstract

The aim of this paper is to give a new proof that any very weak -harmonic function in the unit ball is smooth. As a first step, we improve the local summability properties of . Then, we exploit a suitable version of the difference quotient method tailored to get rid of the singularity of the integral kernel and gain Sobolev regularity and local linear estimates of the norm of . Finally, by applying more standard methods, such as elliptic regularity and Schauder estimates, we reach the real analyticity of . Up to the authors’ knowledge, the difference quotient techniques are new.

Cite this article

Alessandro Carbotti, Simone Cito, Domenico Angelo La Manna, Diego Pallara, Local regularity of very weak -harmonic functions via fractional difference quotients. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. (2025), published online first

DOI 10.4171/RLM/1045