Convex integration and the Lp theory of elliptic equations.
Kari Astala, Daniel Faraco,and László Székelyhidi
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Submission date: 12. Oct. 2004
published in: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 7 (2008) 1, p. 1-50
DOI number (of the published article): 10.2422/2036-2145.2008.1.01
MSC-Numbers: 30C62, 35D10, 39J40
Keywords and phrases: quasiconformal mappings, convex integration, higher integrability
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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.