Asymptotic expansions and unique continuation at Dirichlet-Neumann boundary junctions for planar elliptic equations

Mouhamed Moustapha Fall; Veronica Felli; Alberto Ferrero; Alassane Niang; Mouhamed Moustapha Fall; Veronica Felli; Alberto Ferrero; Alassane Niang

doi:10.3934/Mine.2018.1.84

Mathematics in Engineering

2019, Volume 1, Issue 1: 84-117. doi: 10.3934/Mine.2018.1.84

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Research article

Asymptotic expansions and unique continuation at Dirichlet-Neumann boundary junctions for planar elliptic equations

1.
African Institute for Mathematical Sciences (A.I.M.S.) of Senegal, KM 2, Route de Joal, AIMS-Senegal, B.P. 1418. Mbour, Senegal
2.
Università di Milano-Bicocca, Dipartimento di Scienza dei Materiali, Via Cozzi 55, 20125 Milano,Italy
3.
Università degli Studi del Piemonte Orientale, Dipartimento di Scienze e Innovazione Tecnologica, Viale Teresa Michel 11, 15121 Alessandria, Italy
4.
Université Cheikh Anta Diop, BP 16 889 Dakar-Fann, Senegal

Received: 08 June 2018 Accepted: 16 August 2018 Published: 21 September 2018

We consider elliptic equations in planar domains with mixed boundary conditions of Dirichlet-Neumann type. Sharp asymptotic expansions of the solutions and unique continuation properties from the Dirichlet-Neumann junction are proved.
- mixed boundary conditions,
- unique continuation,
- asymptotic expansion,
- monotonicity formula
Citation: Mouhamed Moustapha Fall, Veronica Felli, Alberto Ferrero, Alassane Niang. Asymptotic expansions and unique continuation at Dirichlet-Neumann boundary junctions for planar elliptic equations[J]. Mathematics in Engineering, 2019, 1(1): 84-117. doi: 10.3934/Mine.2018.1.84

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Abstract

We consider elliptic equations in planar domains with mixed boundary conditions of Dirichlet-Neumann type. Sharp asymptotic expansions of the solutions and unique continuation properties from the Dirichlet-Neumann junction are proved.

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