Coercivity of the single layer heat potential. (English) Zbl 0672.65092

This note treats a single layer heat potential operator. This operator is shown to map a certain anisotropic Sobolev space isomorphically onto its dual. Moreover the coercivity estimate is obtained. The well-posedness of the operator equation provides the quasioptimality of the Galerkin approximations.
Reviewer: V.Drápalík


65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65R20 Numerical methods for integral equations
35K05 Heat equation
35C15 Integral representations of solutions to PDEs
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)