THE BAIRE METHOD FOR THE PRESCRIBED SINGULAR VALUES PROBLEM

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.