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JOURNALS // Ufimskii Matematicheskii Zhurnal // Archive

Ufimsk. Mat. Zh., 2024 Volume 16, Issue 4, Pages 53–76 (Mi ufa716)

Existence and uniqueness of solutions to outer Zaremba problem for elliptic equations with measure–valued potential

F. Kh. Mukminova, O. S. Stekhunb

a Institute of Mathematics with Computing Centre, Ufa Federal Research Centre, Russian Academy of Sciences, Ufa
b Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: In the exterior of a ball in the space $\mathbb{R}^n$ we consider the Zaremba and Neumann problems for quasilinear second order elliptic problems with a measure–valued potential. We proved the existence and uniqueness of entropy solution to the Zaremba and Neumann problems.

Keywords: nonlinear elliptic equation, entropy solution, Radon measure, Zaremba problem.

UDC: 517.956.2

MSC: 35J62, 35J25, 35A01, 35A02, 35D99

Received: 18.04.2024


 English version:
Ufa Mathematical Journal, 2024, 16:4, 53–75


© Steklov Math. Inst. of RAS, 2025