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JOURNALS // Funktsional'nyi Analiz i ego Prilozheniya // Archive

Funktsional. Anal. i Prilozhen., 2021 Volume 55, Issue 1, Pages 65–72 (Mi faa3823)

This article is cited in 3 papers

On Numerically Implementable Explicit Formulas for the Solutions to the 2D and 3D Equations $\operatorname{div}(\alpha(w)\nabla w)=0$ and $\operatorname{div}(\beta\nabla w)=0$ with Cauchy Data on an Analytic Boundary

A. S. Demidov

Department of Mathematics and Mechanics, Lomonosov Moscow State University, Moscow, Russia

Abstract: A construction of numerically implementable explicit expressions for the solutions of the two- and three-dimensional equations $\operatorname{div}(\alpha(w)\nabla w)=0$ and $\operatorname{div}(\beta\nabla w)=0$ with Cauchy data on an analytic boundary is presented.

Keywords: Cauchy problem, elliptic equation, explicit formula.

UDC: 517.9

Received: 22.07.2020
Revised: 22.07.2020
Accepted: 17.09.2020

DOI: 10.4213/faa3823


 English version:
Functional Analysis and Its Applications, 2021, 55:1, 52–58

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© Steklov Math. Inst. of RAS, 2026