Fundamental solution of a higher step Grushin type operator

Equations involving a variable exponent Grushin-type operator

In this paper we define a Grushin-type operator with a variable exponent growth and establish existence results for an equation involving such an operator. A suitable function space setting is introduced. Regarding the tools used in proving the existence of solutions for the equation analyzed here they rely on the critical point theory combined with adequate variational techniques. 2010 Mathema...

A Fundamental Solution of N. Zeilon's Operator

Lie-type higher derivations on operator algebras

 Motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study Lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎It is shown‎ ‎that every Lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎The definition of Lie $n$-higher‎ ‎derivations on operator algebras and related pot...

On the Grushin Operator and Hyperbolic Symmetry

Complexity of geometric symmetry for differential operators with mixed homogeniety is examined here. Sharp Sobolev estimates are calculated for the Grushin operator in low dimensions using hyperbolic symmetry and conformal geometry. Considerable interest exists in understanding differential operators with mixed homogeneity. A simple example is the Grushin operator on R ∆G = ∂ ∂t2 + 4t ∂ ∂x2 . T...

Global Attractor for a Semilinear Parabolic Equation Involving Grushin Operator

The aim of this paper is to prove the existence of a global attractor for a semilinear degenerate parabolic equation involving the Grushin operator.