Weighted Poincaré Inequalities for Non-local Dirichlet Forms

Non-local Dirichlet Forms and Symmetric Jump Processes

We consider the symmetric non-local Dirichlet form (E ,F) given by E(f, f) = ∫

New Weighted Integral Inequalities for Differential Forms in Some Domains

Differential forms are interesting and important generalizations of real functions and distributions. Many interesting results and applications of differential forms have recently been found in some fields, such as tensor analysis, potential theory, partial differential equations and quasiregular mappings, see [B], [C], [D1], [HKM], [I], [IL] and [IM]. In many cases, we need to know the integra...

Weighted Inequalities for Potential Operators on Differential Forms

The Allegretto - Piepenbrink Theorem for Strongly Local Dirichlet Forms

The existence of positive weak solutions is related to spectral information on the corresponding partial differential operator. 2000 Mathematics Subject Classification: 35P05, 81Q10 Introduction The Allegretto-Piepenbrink theorem relates solutions and spectra of 2nd order partial differential operators H and has quite some history, cf. [1, 5, 6, 7, 34, 35, 36, 43, 37, 38]. One way to phrase it ...

Non-Symmetric Translation Invariant Dirichlet Forms

In order to treat certain "non-symmetric" potential theories, It6 I-4] and Bliedtner [1] have generalized Beurling and Deny's theory of Dirichlet spaces by replacing the inner product in the Dirichlet space with a bilinear form defined on a real, regular functional space. This bilinear form, called a Dirichlet form, is supposed to be continuous and coercive, and furthermore to satisfy a "contra...