A’priori Estimates and Precise Regularity for Parabolic Systems with Discontinuous Data
نویسنده
چکیده
We deal with linear parabolic (in sense of Petrovskii) systems of order 2b with discontinuous principal coefficients. A’priori estimates in Sobolev and Sobolev– Morrey spaces are proved for the strong solutions by means of potential analysis and boundedness of certain singular integral operators with kernels of mixed homogeneity. As a byproduct, precise characterization of the Morrey, BMO and Hölder regularity is given for the solutions and their derivatives up to order 2b− 1.
منابع مشابه
Discrete maximal parabolic regularity for Galerkin finite element methods
The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the time discontinuous Galerkin solution of linear parabolic equations. Such estimates have many applications. They are essential, for example, in establishing optimal a priori error estimates in nonHilbertian norms without unnatural coupling of spatial mesh sizes with tim...
متن کاملConvergence of Discontinuous Time-stepping Schemes for a Robin Boundary Control Problem under Minimal Regularity Assumptions
The minimization of the energy functional having states constrained to semi-linear parabolic PDEs is considered. The controls act on the boundary and are of Robin type. The discrete schemes under consideration are discontinuous in time but conforming in space. Stability estimates are presented at the energy norm and at arbitrary times for the state, and adjoint variables. The estimates are deri...
متن کاملError Estimates for Discontinuous Galerkin Time-Stepping Schemes for Robin Boundary Control Problems Constrained to Parabolic PDEs
We consider fully discrete finite element approximations of a Robin optimal boundary control problem, constrained by linear parabolic PDEs with rough initial data. Conforming finite element methods for spatial discretization combined with discontinuous time-stepping Galerkin schemes are being used for the space-time discretization. Error estimates are proved under weak regularity hypotheses for...
متن کاملError Estimates for the Discontinuous Galerkin Methods for Parabolic Equations
We analyze the classical discontinuous Galerkin method for a general parabolic equation. Symmetric error estimates for schemes of arbitrary order are presented. The ideas we develop allow us to relax many assumptions freqently required in previous work. For example, we allow different discrete spaces to be used at each time step and do not require the spatial operator to be self adjoint or inde...
متن کاملOn maximal parabolic regularity for non-autonomous parabolic operators
We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time integrability exponents r 6= 2. This allows us to prove maximal parabolic L r-regularity for discontinuous non-autonomous second-order divergence form ...
متن کامل