Abstract
For a class of functionals having the (p, q)-growth, we establish an improved range of exponents p, q for which the Lavrentiev phenomenon does not occur.
The proof is based on a standard mollification argument and Young convolution inequality. Our contribution is two-fold. First, we observe that it is sufficient to regularise only bounded functions. Second, we exploit the lower bound on the function rather than the L p estimate on the gradient. Our proof does not rely on the properties of minimizers to variational problems but it is rather a consequence of the underlying Musielak-Orlicz function spaces. Moreover, our method works for unbounded boundary data, the variable exponent functionals and vectorial problems.In addition, the result seems to be optimal for p \le d.