Local Hölder and maximal regularity of solutions of elliptic equations with superquadratic gradient terms

Marco Cirant, Gianmaria Verzini

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Abstract

We study the local Hölder regularity of strong solutions u of second-order uniformly elliptic equations having a gradient term with superquadratic growth γ>2, and right-hand side in a Lebesgue space Lq. When [Formula presented] (N is the dimension of the Euclidean space), we obtain the optimal Hölder continuity exponent [Formula presented]. This allows us to prove some new results of maximal regularity type, which consist in estimating the Hessian matrix of u in Lq. Our methods are based on blow-up techniques and a Liouville theorem.
Original languageEnglish (US)
Pages (from-to)108700
JournalAdvances in Mathematics
Volume409
DOIs
StatePublished - Sep 21 2022
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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