On Green's Functions and Positive, Self-Adjoint, Elliptic Differential Operators
David Raske
TL;DR
This paper discusses the properties of Green's functions, heat kernels, and eigenvalues related to higher-order elliptic differential operators, focusing on their positivity and spectral characteristics.
Contribution
It introduces a detailed analysis of positivity conditions for Green's functions and heat kernels in the context of higher-order elliptic operators.
Findings
Conditions for positivity of Green's functions identified
Relationships between heat kernels and eigenvalues established
Implications for spectral theory of elliptic operators discussed
Abstract
This paper is being replaced by another of the author's that contains a brief summary of the problem of positivity of Green's functions, heat kernels, and principal eigenvalues of higher-order elliptic differential operators.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems