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

TL;DR

This paper investigates elliptic equations with mixed boundary conditions in planar domains, providing sharp asymptotic expansions of solutions and establishing unique continuation properties at Dirichlet-Neumann boundary junctions.

Contribution

It introduces precise asymptotic expansions and unique continuation results for elliptic equations at boundary junctions, advancing understanding of boundary behavior.

Findings

Sharp asymptotic expansions of solutions near boundary junctions

Unique continuation properties established at Dirichlet-Neumann junctions

Enhanced understanding of boundary behavior in elliptic equations

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.