Rendiconti Lincei - Matematica e Applicazioni

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Volume 31, Issue 2, 2020, pp. 391–399
DOI: 10.4171/RLM/896

Published online: 2020-06-30

Elliptic Venttsel problems with $VMO$ coefficients

Darya E. Apushkinskaya[1], Alexander I. Nazarov[2], Dian K. Palagachev[3] and Lubomira G. Softova[4]

(1) Universität des Saarlandes, Saarbrücken, Germany, RUDN University, Moscow, and St. Petersburg State University, Russia
(2) Steklov Institute of Mathematics of RAS and St. Petersburg State University, Russian Federation
(3) Politecnico di Bari, Italy
(4) Università di Salerno, Italy

We announce new results about strong solvability of linear and quasilinear Venttsel boundary value problems with discontinuous principal coefficients.

Keywords: Second-order elliptic equations, quasilinear, Venttsel problem, $VMO$, $a priori$ estimates, maximal regularity, strong solvability

Apushkinskaya Darya, Nazarov Alexander, Palagachev Dian, Softova Lubomira: Elliptic Venttsel problems with $VMO$ coefficients. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), 391-399. doi: 10.4171/RLM/896