We study the local Holder regularity of strong solutions u of second-order uniformly elliptic equations having a gradient term with superquadratic growth gamma > 2, and right-hand side in a Lebesgue space Lq. When q > N gamma-1 gamma (N is the dimension of the Euclidean space), we obtain the optimal Holder continuity exponent alpha q > gamma-2 gamma-1 . 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.

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

Verzini, Gianmaria
2022-01-01

Abstract

We study the local Holder regularity of strong solutions u of second-order uniformly elliptic equations having a gradient term with superquadratic growth gamma > 2, and right-hand side in a Lebesgue space Lq. When q > N gamma-1 gamma (N is the dimension of the Euclidean space), we obtain the optimal Holder continuity exponent alpha q > gamma-2 gamma-1 . 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.
2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1221193
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