Weighted Poincaré Inequalities and Applications in Domain Decomposition

JOHANNES KEPLER UNIVERSITY LINZ Institute of Computational Mathematics Weighted Poincaré inequalities

Poincaré type inequalities are a key tool in the analysis of partial differential equations. They play a particularly central role in the analysis of domain decomposition and multilevel iterative methods for second-order elliptic problems. When the diffusion coefficient varies within a subdomain or within a coarse grid element, then condition number bounds for these methods based on standard Po...

On weighted isoperimetric and Poincaré-type inequalities

Weighted isoperimetric and Poincaré-type inequalities are studied for κ-concave probability measures (in the hierarchy of convex measures).

Divergence operator and Poincaré inequalities on arbitrary bounded domains

Let Ω be an arbitrary bounded domain of Rn. We study the right invertibility of the divergence on Ω in weighted Lebesgue and Sobolev spaces on Ω, and relate this invertibility to a geometric characterization of Ω and to weighted Poincaré inequalities on Ω. We recover, in particular, well-known results on the right invertibility of the divergence in Sobolev spaces when Ω is Lipschitz or, more ge...

Ar(λ)-WEIGHTED CACCIOPPOLI-TYPE AND POINCARÉ-TYPE INEQUALITIES FOR A-HARMONIC TENSORS

Weighted Poincaré-type Inequalities for Cauchy and Other Convex Measures

Brascamp–Lieb-type, weighted Poincaré-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general κ-concave probability measures (in the hierarchy of convex measures). In analogy with the limiting (infinitedimensional log-concave) Gaussian model, the weighted inequalities fully describe the measure concentration and large deviation properties of...