Degenerate Anisotropic Differential Operators and Applications

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Symmetry group, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation

‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry ...

Degenerate Diffusion Operators Arising in Population Biology

We analyze a class of partial differential equations that arise as"backwards Kolmogorov operators"in infinite population limits of the Wright-Fisher models in population genetics and in mathematical finance. These are degenerate elliptic operators defined on manifolds with corners. The classical example is the Kimura diffusion operator, which acts on functions defined on the simplex in R^n. We ...

On Anisotropic Triebel-lizorkin Type Spaces, with Applications to the Study of Pseudo-differential Operators

A construction of Triebel-Lizorkin type spaces associated with flexible decompositions of the frequency space R is considered. The class of admissible frequency decompositions is generated by a one parameter group of (anisotropic) dilations on R and a suitable decomposition function. The decomposition function governs the structure of the decomposition of the frequency space, and for a very par...

Linear and nonlinear degenerate boundary value problems in Besov spaces

Keywords: Boundary value problems Differential-operator equations Banach-valued Besov spaces Operator-valued multipliers Interpolation of Banach spaces a b s t r a c t The boundary value problems for linear and nonlinear degenerate differential-operator equations in Banach-valued Besov spaces are studied. Several conditions for the separability of linear elliptic problems are given. Moreover, t...