In this paper we prove that solutions to a transmission problem degenerating on the interface are Hölder differentiable up to the interface with universal estimates. Furthermore, we obtain a sharper pointwise C^{1,α(·)} with optimal variable exponent and uniform estimates. Our results also establish a comprehensive theory for degenerate transmission problems with flat interfaces, covering the existence, comparison principle and uniqueness of solutions.
Giovagnoli, D., Jesus, D. (2026). A fully nonlinear transmission problem degenerating on the interface. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 65(3), 1-28 [10.1007/s00526-025-03237-6].
A fully nonlinear transmission problem degenerating on the interface
Giovagnoli, Davide;
2026
Abstract
In this paper we prove that solutions to a transmission problem degenerating on the interface are Hölder differentiable up to the interface with universal estimates. Furthermore, we obtain a sharper pointwise C^{1,α(·)} with optimal variable exponent and uniform estimates. Our results also establish a comprehensive theory for degenerate transmission problems with flat interfaces, covering the existence, comparison principle and uniqueness of solutions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
