A Reilly Formula and Eigenvalue Estimates for Differential Forms

Weighted Decomposition Estimates for Differential Forms

Let e1, e2, . . . , en denote the standard orthogonal basis of R. Suppose that Λ Λ R is the linear space of all l-vectors, spanned by the exterior product eI ei1∧ei2∧· · ·∧eil corresponding to all ordered l-tuples I i1, i2, . . . , il , 1 ≤ i1 < i2 < · · · < il ≤ n. Throughout this paper, we always assume that Ω is an open subset of R. We use D′ M,Λ to denote the space of all differential l-for...

Some Caccioppoli Estimates for Differential Forms

Differential forms on locally convex spaces and the Stokes formula

We prove a version of the Stokes formula for differential forms on locally convex spaces announced in [10]. The main tool used for proving this formula is the surface layer theorem proved in the paper [6] by the author. Moreover, for differential forms of a Sobolev-type class relative to a differentiable measure [1], we compute the operator adjoint to the exterior differential in terms of stand...

Estimates of Weighted Hardy-Littlewood Inequality for Differential Forms

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. As an important tool the Hardy-Littlewood inequality have been playing critical roles in many mathematics, including potential analysis, partial differential equations and the theory of elas...

Limiting Fractional and Lorentz Spaces Estimates of Differential Forms

We obtain estimates in Besov, Lizorkin-Triebel and Lorentz spaces of differential forms on Rn in terms of their L norm.