Inhomogeneous Gevrey Ultradistributions and Cauchy Problem

Inhomogeneous Two-Parameter Abstract Cauchy Problem

The Gevrey Hypoellipticity for Linear and Non-linear Fokker-planck Equations

Recently, a lot of progress has been made on the study for the spatially homogeneous Boltzmann equation without angular cutoff, cf. [2, 3, 8, 22] and references therein, which shows that the singularity of collision cross-section yields some gain of regularity in the Sobolev space frame on weak solutions for Cauchy problem. That means, this gives the C regularity of weak solution for the spatia...

Eigenfunction Expansions of Ultradifferentiable Functions and Ultradistributions

In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold X. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on X. This extends the result for analytic functions on compact manifold by Seeley [See69], and the characterisation of Gevrey functions and Gevrey u...

Stratified Whitney jets and tempered ultradistributions on the subanalytic site

In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold X. Then we define stratified ultradistributions of Beurling and Roumieu type on X. In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if X is a real surface, the tempered...

Schwarz boundary problem on a triangle

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...