Hypoellipticity for Linear Degenerate Elliptic Systems in Carnot Groups and Applications

Regularity Results for Quasilinear Degenerate Elliptic Obstacle Problems in Carnot Groups

Let {X1, . . . , Xm} be a basis of the space of horizontal vector fields on the Carnot group G = (R , ◦)(m < N). We establish regularity results for solutions to the following quasilinear degenerate elliptic obstacle problem ∫ Ω 〈〈AXu,Xu〉 p−2 2 AXu,X(v − u)〉dx ≥ ∫ Ω B(x, u,Xu)(v − u)dx

On Local Properties of Some Classes of Infinitely Degenerate Elliptic Differential Operators

We give necessary and sufficient conditions for local solvability and hypoellipticity of some classes of infinitely degenerate elliptic differential operators.

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

Some local fixed point results under $C$-class functions with applications to coupled elliptic systems

The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved herein generalize, modify and unify some recent results of the existing literature. As an ...

New variants of the global Krylov type methods for linear systems with multiple right-hand sides arising in elliptic PDEs

In this paper, we present new variants of global bi-conjugate gradient (Gl-BiCG) and global bi-conjugate residual (Gl-BiCR) methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. It is shown that these new algorithms converge faster and more smoothly than the Gl-...