Unexpected solutions of first and second order partial differential equations

Stefan Müller and Vladimír Sverák

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Submission date: 18. Oct. 1998
Pages: 17
published in: Documenta mathematica, Extra Volume ICM 1998, II (1998), p. 691-702 
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Abstract:
We discuss a general approach to construct Lipschitz solutions of , where and where K is a given set of matrices. The approach is an extension of Gromov's method of convex integration. One application concerns variational problems that arise in models of microstructure in solid-solid phase transitions. Another application is the systematic construction of singular solutions of elliptic systems. In particular, there exists a (variational) second order strongly elliptic system that admits a Lipschitz solution which is nowhere .