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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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