In this article we study functionals of the type considered in [36], i.e. here , and . We prove the optimal regularity of minimizers of the functional indicated above (with precise estimates) when the coefficients are continuous functions and for some , with and Q bounded. We do this by presenting a new compactness argument and approximation theory similar to the one developed by L. Caffarelli in [9] to treat the regularity theory for solutions to fully nonlinear PDEs. Moreover, we introduce the operator that allows one to transfer minimizers from the transmission problems to the Alt-Caffarelli-Friedman type functionals, in small scales, allowing this way the study of the regularity theory of minimizers of Bernoulli type free transmission problems.
Moreira, D., Shrivastava, H. (2023). Optimal regularity for variational solutions of free transmission problems. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, 169, 1-49 [10.1016/j.matpur.2022.11.005].
Optimal regularity for variational solutions of free transmission problems
Moreira, Diego;
2023
Abstract
In this article we study functionals of the type considered in [36], i.e. here , and . We prove the optimal regularity of minimizers of the functional indicated above (with precise estimates) when the coefficients are continuous functions and for some , with and Q bounded. We do this by presenting a new compactness argument and approximation theory similar to the one developed by L. Caffarelli in [9] to treat the regularity theory for solutions to fully nonlinear PDEs. Moreover, we introduce the operator that allows one to transfer minimizers from the transmission problems to the Alt-Caffarelli-Friedman type functionals, in small scales, allowing this way the study of the regularity theory of minimizers of Bernoulli type free transmission problems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
