Functions with presribed singular values of the gradient |
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| Authors: | Pietro Celada Stefania Perrotta |
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| Institution: | (1) Dipartimento die Scienze Matematiche, Università degli Studi di Trieste, P.le Europa 1, I-34127 Trieste, Italy. E-mail: celada@univ.trieste.it, IT;(2) Dipartimento die Matematica Pura ed Applicata "G. Vitali", Università degli Studi di Modena, Via Campi 213/B, I-41100 Modena, Italy. E-mail: perrotta@c220.unimo.it, IT |
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| Abstract: | We prove the existence of infinitely many vector-valued Lipschitz-continuous functions u on an open set satisfying suitable Dirichlet boundary conditions such that the singular values of the gradient matrix
u, i.e. the square roots of the eigenvalues of the symmetrized matrix , agree a.e. on with N given positive, bounded and lower semicontinuous functions.
Received May 28, 1997 |
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