# Hilbert-Schmidt regularity of symmetric integral operators on bounded domains with applications to SPDE approximations

@article{Kovacs2021HilbertSchmidtRO, title={Hilbert-Schmidt regularity of symmetric integral operators on bounded domains with applications to SPDE approximations}, author={Mih'aly Kov'acs and Annika Lang and Andreas Petersson}, journal={ArXiv}, year={2021}, volume={abs/2107.10104} }

Regularity estimates for an integral operator with a symmetric continuous kernel on a convex bounded domain are derived. The covariance of a mean-square continuous random field on the domain is an example of such an operator. The estimates are of the form of Hilbert–Schmidt norms of the integral operator and its square root, composed with fractional powers of an elliptic operator equipped with homogeneous boundary conditions of either Dirichlet or Neumann type. These types of estimates have… Expand

#### One Citation

Approximation of SPDE covariance by finite elements

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The problem of approximating the covariance operator of the mild solution to a linear stochastic partial differential equation is considered. An integral equation involving the semigroup of the mild… Expand

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