Local Boundedness of Minimizers of Anisotropic Functionals (Journal of Partial Differential Equations, 1995)
Using the theory of anisotropic Sobolev spaces, we discuss in this paper the relation between the growth conditions and the local boundedness of minimizers of an anisotropic variational problem. This thoroughly explains the counterexample due to Giaquinta (1987). In the sense of local boundedness, we point out a critical index.
Keywords: Variational problem; anisotropic Sobolev spaces; local bounded ness; minimizers