Variational inequalities with thin obstacles and Signorini-type boundary conditions are classical problems in the calculus of variations, arising in numerous applications. In the linear case many refined results are known, while in the nonlinear setting our understanding is still at a preliminary stage. In this paper we prove C1 regularity for the solutions to a general class of quasi-linear variational inequalities with thin obstacles and C1,α regularity for variational inequalities under Signorini-type conditions on the boundary of a domain.
Regularity of solutions to nonlinear thin and boundary obstacle problems / DI FAZIO, Luca. - (2021 Dec 17).
Regularity of solutions to nonlinear thin and boundary obstacle problems
DI FAZIO, LUCA
17/12/2021
Abstract
Variational inequalities with thin obstacles and Signorini-type boundary conditions are classical problems in the calculus of variations, arising in numerous applications. In the linear case many refined results are known, while in the nonlinear setting our understanding is still at a preliminary stage. In this paper we prove C1 regularity for the solutions to a general class of quasi-linear variational inequalities with thin obstacles and C1,α regularity for variational inequalities under Signorini-type conditions on the boundary of a domain.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.