Sentence examples for maximal regularity of from inspiring English sources

We present a complete Lp-theory for such problems which is based on maximal regularity of certain model problems.

We prove maximal regularity of type Lp Lq for operators in non-divergence form with complex-valued measurable coefficients on Rn.

We prove that the boundedness of a special type of operator valued H∞-calculus is sufficient for maximal regularity of the solution.

As recently shown by the author, the analyticity of T is a necessary condition for the maximal regularity of the discrete time evolution equation un+1−Tun=fn for all n∈Z+, u0=0.

These results are discrete analogues of the corresponding results for the maximal regularity of the evolution equation u′(t)−Au(t)=f(t) for all t∈R+, u(0)=0, due to Lamberton, Weis, Coulhon and Duong and Hieber and Prüss.

shows the maximal regularity of the operator.

(xi) denotes all maps possessing the property of maximal     regularity on with respect to, that is, given, the initial problem.

For instance, the boundedness of Fourier multiplier operators plays a crucial role in the theory of linear PDE's, especially in the study of maximal regularity for elliptic and parabolic PDE's.

The crucial parts of the proof are to employ the end-point type of maximal regularity for the homogeneous heat equation and some new bilinear estimates in the Hardy space.

In this direction one of the authors in [18] considered maximal regularity for Volterra difference equations with infinite delay.

We apply our main result to maximal regularity for Cauchy problems involving A.