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Minimal regularity of the solutions of some transmission problems
Author(s) -
Mercier D.
Publication year - 2003
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.356
Subject(s) - mathematics , monotonic function , vertex (graph theory) , operator (biology) , constant (computer programming) , laplace transform , transmission (telecommunications) , boundary value problem , boundary (topology) , mathematical analysis , upper and lower bounds , pure mathematics , combinatorics , graph , biochemistry , chemistry , repressor , computer science , transcription factor , gene , programming language , electrical engineering , engineering
We consider some transmission problems for the Laplace operator in two‐dimensional domains. Our goal is to give minimal regularity of the solutions, better than H 1 , with or without conditions on the (positive) material constants. Under a monotonicity or quasi‐monotonicity condition on the constants (or on the inverses according to the boundary conditions), we study the behaviour of the solution near vertex and near interior nodes and show in each case that the given regularity is sharp. Without condition we prove that the regularity near a corner is of the form H 1+ρ , where ρ is a given bound depending on the material constants. Numerical examples are presented which confirm the sharpness of our lower bounds. Copyright © 2003 John Wiley & Sons, Ltd.