Titlebook: Methods of Mathematical Physics; Classical and Modern Alexey N. Karapetyants,Vladislav V. Kravchenko Textbook 2022 The Editor(s) (if applic

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Boundary Value Problems for the Heat Equation,One of the aims of this chapter is to prove the uniqueness theorems for some fundamental boundary value problems for the heat equation. Since their proof is based on the maximum (minimum) principle for solutions of the heat equation, we begin by deducing this principle.

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Harmonic Functions and Their Properties,As one can observe, there is a profound difference between the two-dimensional (. = 2) and the multidimensional (. ≥ 3) situations. This difference radicates in the fact that the fundamental solution of the Laplace operator in a two-dimensional case has two singular points: zero and infinity, which is not the case for higher dimensional cases.

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Potential Theory,We begin by considering some analogies from field theory.

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Textbook 2022oduced to a variety of methods that reflect current trends in research, including the Bergman kernel approach for solving boundary value and spectral problems for PDEs with variable coefficients. With its careful treatment of the fundamentals as well as coverage of topics not often encountered in te

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