Spherical Means for PDEs (1st edition.)

This monograph presents new spherical mean-value relations for classical boundary-value problems of mathematical physics.

The derived spherical mean value relations provide equivalent integral formulations of original boundary-value problems.;Direct and converse mean-value theorems are proved for scalar elliptic equations (the Laplace, Helmholtz and diffusion equations), parabolic equations, high-order elliptic equations (biharmonic and metaharmonic equations), and systems of elliptic equations (the Lame equation, systems of diffusion and elasticity equations).

In addition, applications to the random-walk-on-spheres method are given.;The book should be of interest to postgraduate researchers in the field of partial differential and integral equations, numerical mathematics and applied probability, as well as mathematical physics.