EXISTENCE AND REGULARITY OF SOLUTIONS FOR THE ELLIPTIC NONLINEAR TRANSPARENT MEDIA EQUATION - Balducci, Francesco; Oliva, Francescantonio; Petitta, Francesco; Stapenhorst, Matheus F. [UNESP] (My University, 2025)
In this paper we study existence and regularity of solutions to Dirichlet problems as (Formula presented) where Ω is an open bounded subset of RN (N ≥ 2) with Lipschitz boundary, m > 0, and f belongs to the Lorentz space LN,∞(Ω). In particular, we explore the regularizing effect given by the degenerate coefficient |u|m in order to get non-trivial and bounded solutions with no smallness assumptions on the size of the data.
Keywords: Nonlinear elliptic equations; Torsion problem; Total variation; Transparent media equation