On a necessary condition in the calculus of variations in Sobolev spaces with variable exponent
Volume 41 / 2014
Applicationes Mathematicae 41 (2014), 165-174
MSC: 46E35, 49K21, 91G80.
DOI: 10.4064/am41-2-4
Abstract
We prove an approximation theorem in generalized Sobolev spaces with variable exponent $W^{1,p(\cdot )}(\varOmega )$ and we give an application of this approximation result to a necessary condition in the calculus of variations.
