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Quadratic tilt-excess decay and strong maximum principle for varifolds

Reiner Schätzle (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper, we prove that integral n -varifolds μ in codimension 1 with H μ L loc p ( μ ) , p > n , p 2 have quadratic tilt-excess decay tiltex μ ( x , ϱ , T x μ ) = O x ( ϱ 2 ) for μ -almost all x , and a strong maximum principle which states that these varifolds cannot be touched by smooth manifolds whose mean curvature is given by the weak mean curvature H μ , unless the smooth manifold is locally contained in the support of μ .

Quasiharmonic fields and Beltrami operators

Claudia Capone (2002)

Commentationes Mathematicae Universitatis Carolinae

A quasiharmonic field is a pair = [ B , E ] of vector fields satisfying div B = 0 , curl E = 0 , and coupled by a distorsion inequality. For a given , we construct a matrix field 𝒜 = 𝒜 [ B , E ] such that 𝒜 E = B . This remark in particular shows that the theory of quasiharmonic fields is equivalent (at least locally) to that of elliptic PDEs. Here we stress some properties of our operator 𝒜 [ B , E ] and find their applications to the study of regularity of solutions to elliptic PDEs, and to some questions of G-convergence.

Quasilinear elliptic problems with multivalued terms

Nikolaos Halidias, Nikolaos S. Papageorgiou (2000)

Czechoslovak Mathematical Journal

We study the quasilinear elliptic problem with multivalued terms.We consider the Dirichlet problem with a multivalued term appearing in the equation and a problem of Neumann type with a multivalued term appearing in the boundary condition. Our approach is based on Szulkin’s critical point theory for lower semicontinuous energy functionals.

Quasireverse Hölder inequalities and a priori estimates for strongly nonlinear systems

Arina A. Arkhipova (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

It is proved that a function can be estimated in the norm with a higher degree of summability if it satisfies some integral relations similar to the reverse Hölder inequalities (quasireverse Hölder inequalities). As an example, we apply this result to derive an a priori estimate of the Hölder norm for a solution of strongly nonlinear elliptic system.

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