Regularity Of Parabolic Problems Research Articles

On the $\ell^s$-boundedness of a family of integral operators

In this paper we prove an \ell^s -boundedness result for integral operators with operator-valued kernels. The proofs are based on extrapolation techniques with weights due to Rubio de Francia. The results will be applied by the first and third author in a subsequent paper where a new approach to maximal L^p -regularity for parabolic problems with time-dependent generator is developed.

Maximal [formula omitted]-regularity of parabolic problems with boundary dynamics of relaxation type

In this paper we investigate vector-valued parabolic initial boundary value problems of relaxation type. Typical examples for such boundary conditions are dynamic boundary conditions or linearized free boundary value problems like in the Stefan problem. We present a complete L p -theory for such problems which is based on maximal regularity of certain model problems.