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Distributional analysis of boundary value problems in half‐spaces – exemplified by Melan's problem of elastostatics
Author(s) -
Kirchner G.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310025
Subject(s) - mathematics , uniqueness , convolution (computer science) , boundary value problem , computation , matrix (chemical analysis) , variable (mathematics) , function (biology) , mathematical analysis , representation (politics) , pure mathematics , computer science , materials science , algorithm , machine learning , evolutionary biology , artificial neural network , composite material , biology , politics , political science , law
Using a result on the ${\cal C}^\infty$ ‐dependence (with respect to a distinguished variable) of solutions to partially hypoelliptic operators, we present a definition for Green's function which allows to prove a representation theorem. Afterwards we discuss the construction of a Green's matrix for Melan's problem of elastostatics using the reflection principle and single layer potentials. This involves the solution of convolution equations as well as the explicit computation of convolutions. In this special case also the question of uniqueness is investigated.