A fractional Gehring lemma, with applications to nonlocal equations

Tuomo Kuusi (1) , Giuseppe Mingione (2) , Yannick Sire (3)

1 Department of Mathematics [Aalto]
2 Dipartimento di Matematica e Informatica [Parma]
3 I2M - Institut de Mathématiques de Marseille

We describe a fractional version of the classical Gehring lemma. As a consequence, new self-improving regularity properties of solutions to integrodifferential equations emerge.

Mots clés: self-improving properties; non-local operators; elliptic equations

Domaines: Equations aux dérivées partielles [math.AP]

Tuomo Kuusi, Giuseppe Mingione, Yannick Sire. A fractional Gehring lemma, with applications to nonlocal equations. Rendiconti Lincei. Matematica e Applicazioni, 2014, 25 (4), pp.345--358. ⟨10.4171/RLM/683⟩. ⟨hal-01341556⟩