Preprint 42/1998

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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We discuss a general approach to construct Lipschitz solutions of tex2html_wrap_inline9, where tex2html_wrap_inline11 and where K is a given set of tex2html_wrap_inline15 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 tex2html_wrap_inline17 (variational) second order strongly elliptic system tex2html_wrap_inline19 that admits a Lipschitz solution which is nowhere tex2html_wrap_inline21.

24.11.2021, 02:10