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MiS Preprint
70/2004

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

Kari Astala, Daniel Faraco and László Székelyhidi

Abstract

We consider elliptic partial differential equations and provide a method constructing solutions with critical integrability properties. We illustrate the technique by studying isotropic equations and equations in non-divergence form in the plane.

Received:
Oct 12, 2004
Published:
Oct 12, 2004
MSC Codes:
30C62, 35D10, 39J40
Keywords:
quasiconformal mappings, convex integration, higher integrability

Related publications

inJournal
2008 Repository Open Access
Kari Astala, Daniel Faraco and László Székelyhidi

Convex integration and the \({L}^{p}\) theory of elliptic equations

In: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 7 (2008) 1, pp. 1-50