D. E. Apushkinskaya, A. I. Nazarov, D. K. Palagachev, L. G. Softova, “The quasilinear parabolic Venttsel' problem with discontinuous leading coefficients”, Funktsional. Anal. i Prilozhen., 2023, Volume 57, Issue 2,Pages <nobr>93

This article is cited in 2 papers

Brief communications

The quasilinear parabolic Venttsel' problem with discontinuous leading coefficients

D. E. Apushkinskaya^ab, A. I. Nazarov^ac, D. K. Palagachev^d, L. G. Softova^e

^a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
^b Peoples Friendship University of Russia
^c Saint Petersburg State University
^d Politecnico di Bari
^e Università degli Studi di Salerno (UNISA), Salerno, Italy

Abstract: New results on the strong solvability in Sobolev spaces of the quasilinear Venttsel' problem for parabolic equations with discontinuous leading coefficients are obtained.

Keywords: quasilinear second-order parabolic equation, Venttsel' problem, $VMO_x$ class, a priori estimate, existence theorem.

Received: 11.02.2023
Revised: 11.02.2023
Accepted: 28.02.2023

DOI: 10.4213/faa4098