Open AccessVarious Kernels in the Theory of Partial Differential Equations
Author(s) -
Stefan Bergman,
M. Schiffer
Publication year - 1950
Publication title -
proceedings of the national academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.36.10.559
Subject(s) - induced pluripotent stem cell , myocyte , cardiac electrophysiology , stem cell , cardiac cell , in vitro , neuroscience , microbiology and biotechnology , drug discovery , contraction (grammar) , cell , cardiac muscle , electrophysiology , computational biology , biomedical engineering , biophysics , chemistry , biology , bioinformatics , anatomy , medicine , embryonic stem cell , biochemistry , endocrinology , gene
and observe that E(u) = E{u, u) is the energy integral connected with (1). Let Z be the linear space of all solutions of (1) with finite energy integral; we may introduce into 2Z the metric based on the scalar product (2) and consider 2. as a Hilbert space. Let N(P, Q) and G(P, Q) denote Neumann's and Green's functions of the differential equation (1) with respect to D. One shows easily that for each function u e Z there holds:
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