VOLUME 19 NUMBER 2 (July to December 2026)

Renormalized solution to a class of elliptic equations in a two-component domain with nonlinear imperfect transmission

In this article, we prove the existence and uniqueness of a renormalized solution of a class of elliptic problems posed in a two-component domain Ω⊆R^N,N≥2 with L^1 data. On the interface, we prescribe that the jump of the solution is related to the flux nonlinearly.

Existence is proved by a classical approximation argument: we introduce an approximate problem and show that its solutions converge to a renormalized solution. The uniqueness result requires certain strict monotonicityconditions and an additional interface regularity lemma.