Milton's conjecture on the regularity of solutions to isotropic equations
Geometric rigidity of conformal matrices
We provide a geometric rigidity estimate à la Friesecke-James-Müller for conformal matrices. Namely, we replace by an arbitrary compact set of conformal matrices, bounded away from and invariant under , and rigid motions by Möbius transformations.
Convex integration and the theory of elliptic equations
This paper deals with the 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 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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