The baire method for the prescribed singular values problem

• Autores: F. S. De Blasi, G. Pianigiani
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 70, Nº 3, 2004, págs. 719-734
• Idioma: inglés
• DOI: 10.1112/s0024610704005599
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• Resumen

  • The paper investigates the vectorial Dirichlet problem defined by Here is an open bounded subset of with boundary , and () denote the singular values of the gradient . The existence of solutions is established under one of the following assumptions: is continuous on and locally contractive on , or is contractive on . This extends a result due to Dacorogna and Marcellini. The approach is based on the Baire category method developed earlier by the authors.