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Milton's conjecture on the regularity of solutions to isotropic equations

Daniel Faraco — 2003

Annales de l'I.H.P. Analyse non linéaire

Geometric rigidity of conformal matrices

Daniel Faraco; Xiao Zhong — 2005

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We provide a geometric rigidity estimate à la Friesecke-James-Müller for conformal matrices. Namely, we replace $SO (n)$ by an arbitrary compact set of conformal matrices, bounded away from $0$ and invariant under $SO (n)$ , and rigid motions by Möbius transformations.

Convex integration and the $L^{p}$ theory of elliptic equations

Kari Astala; Daniel Faraco; László Székelyhidi Jr. — 2008

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

This paper deals with the $L^{p}$ theory of linear elliptic partial differential equations with bounded measurable coefficients. We construct in two dimensions examples of weak and so-called very weak solutions, with critical integrability properties, both to isotropic equations and to equations in non-divergence form. These examples show that the general $L^{p}$ theory, developed in [1, 24] and [2], cannot be extended under any restriction on the essential range of the coefficients. Our constructions are based...

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Currently displaying 1 – 3 of 3

Milton's conjecture on the regularity of solutions to isotropic equations

Geometric rigidity of conformal matrices

Convex integration and the L p theory of elliptic equations

Convex integration and the $L^{p}$ theory of elliptic equations