Hardy-type inequalities related to degenerate elliptic differential operators

Hardy Type Inequalities Related to Degenerate Elliptic Differential Operators

We prove some Hardy type inequalities related to quasilinear second order degenerate elliptic differential operators Lpu := −∇ ∗ L(|∇Lu| ∇Lu). If φ is a positive weight such that −Lpφ ≥ 0, then the Hardy type inequality c ∫ Ω |u| φp |∇Lφ| p dξ ≤ ∫

Degenerate P-laplacian Operators on H-type Groups and Applications to Hardy Type Inequalities

Abstract. Let G be a step-two nilpotent group of H-type with Lie algebra G = V ⊕ t. We define a class of vector fields X = {Xj} on G depending on a real parameter k ≥ 1, and we consider the corresponding p-Laplacian operator Lp,ku = divX(|∇Xu| ∇Xu). For k = 1 the vector fields X = {Xj} are the left invariant vector fields corresponding to an orthonormal basis of V , for k = 2 and G being the He...

Optimal Hardy inequalities for general elliptic operators with improvements

Necessary and sufficient conditions on V are obtained (in terms of the solvability of a linear pde) for (3) to hold. Analogous results involving improvements are obtained for the weighted versions. We establish optimal inequalities which are similar to (1) and are valid for u ∈ H(Ω). We obtain results on improvements of this inequality which are similar to the above results on improvements. In ...

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

Optimal Hardy–littlewood Type Inequalities for Polynomials and Multilinear Operators

Abstract. In this paper we obtain quite general and definitive forms for Hardy–Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to show that in most cases the exponents involved are optimal. The technique we used is a combination of probabilistic tools and of an interpolative a...