D. E. Apushkinskaya, A. I. Nazarov, D. K. Palagachev, L. G. Softova, “Nonstationary venttsel problem with <nobr>$VMO_x$</nobr> leading coefficients”, Dokl. RAN. Math. Inf. Proc. Upr., 2023, Volume 510,Pages <nobr>13

This article is cited in 2 papers

MATHEMATICS

Nonstationary venttsel problem with $VMO_x$ 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, St. Petersburg, Russia
^b Peoples' Friendship University of Russia, Moscow, Russia
^c Saint Petersburg State University, St. Petersburg, Russia
^d Politecnico di Bari, Bari, Italy
^e University of Salerno, Fisciano, Italy

Abstract: We obtain some new results on strong solvability in the Sobolev spaces of the linear Venttsel initial-boundary value problems to parabolic equations with discontinuous leading coefficients.

Keywords: linear second-order parabolic equations, Venttsel problem, class $VMO_x$, a priori estimates, solvability, uniqueness.

UDC: 517.95

Presented: S. V. Kislyakov
Received: 30.11.2022
Revised: 21.02.2023
Accepted: 24.02.2023

DOI: 10.31857/S2686954322600707