Karl K. Sabelfeld & Irina A. Shalimova 
Spherical and Plane Integral Operators for PDEs [PDF ebook] 
Construction, Analysis, and Applications

The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.

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