On a Range of Exponents for Absence of Lavrentiev Phenomenon for Double Phase Functionals

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