Regularity of minimizers for free-discontinuity problems with p()-growth

Article Mathematics, Applied

Lipschitz regularity of minimizers of variational integrals with variable exponents

Michela Eleuteri et al.

Summary: In this paper, we establish the Lipschitz regularity for local minimizers of convex variational integrals. The main novelty lies in assuming an almost critical regularity for the energy density as a function of the x variable in the Orlicz Sobolev setting.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2023)

Add to Collection

Article Mathematics, Applied

Integral representation and G-convergence for free-discontinuity problems with p(.)-growth

Giovanni Scilla et al.

Summary: An integral representation result for free-discontinuity energies on the space GSBV(p(.)) with variable exponent p(x) under the assumption of log-Hölder continuity is proved. The analysis is based on a variable exponent version of the global method for relaxation devised by Bouchitté et al. (Arch Ration Mech Anal 165:187-242, 2002) for a constant exponent. G-convergence of sequences of energies of the same type is proven, limit integrands are identified using asymptotic cell formulas, and a non-interaction property between bulk and surface contributions is proved.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2023)

Add to Collection

Article Mathematics, Applied

Maximal regularity for local minimizers of non-autonomous functionals

Peter Hasto et al.

Summary: This study establishes a sharp and general regularity theory for functionals, solving an open problem since the 1980s. Unlike previous results, a concise way of expressing the continuity requirement is used, applicable to various growth conditions.

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY (2022)

Add to Collection

Article Mathematics, Applied