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

Marco Cirant, Gianmaria Verzini

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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

Bibliographical note

KAUST Repository Item: Exported on 2022-10-07
Acknowledged KAUST grant number(s): CRG2021-4674
Acknowledgements: The authors are members of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). Work partially supported by the project Vain-Hopes within the program VALERE-Università degli Studi della Campania “Luigi Vanvitelli”, by the Portuguese government through FCT/Portugal under the project PTDC/MAT-PUR/1788/2020, and by the King Abdullah University of Science and Technology (KAUST) project CRG2021-4674 “Mean-Field Games: models, theory, and computational aspects”.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • General Mathematics

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