Hopf's boundary type behavior for an interface problem

Maryam Beygmohammadi; Guido Sweers

doi:10.4134/JKMS.j150715

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2017; 54(1): 249-265

Online first article December 6, 2016 Printed January 1, 2017

https://doi.org/10.4134/JKMS.j150715

Hopf's boundary type behavior for an interface problem

Maryam Beygmohammadi and Guido Sweers

University of Cologne, University of Cologne

Abstract

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Abstract

Interface problem here refers to a second order elliptic problem with a discontinuous coefficient for the second order derivatives. For the corresponding boundary value problem, the maximum principle still holds but Hopf's boundary point lemma may fail. We will give an optimal power type estimate that replaces Hopf's lemma at those boundary points, where this coefficient jumps.

Keywords: Hopf's lemma, interface, optimal estimate

MSC numbers: 35J15, 35B51