45 citations · 91 across the 16 of their papers we have counts for
19 papers
Regularity for monotone Operators and applications to homogenization of -Laplace type equations
Lukas Koch, Mathias Schäffner
In this manuscript, we provide local -estimates for the gradient of solutions of a class of quasilinear equations whose principal part lacks strong monotonicity. These estimat…
Upper bounds for the homogenization problem in nonlinear elasticity: the incompressible case
Matthias Ruf, Mathias Schäffner
We consider periodic homogenization of hyperelastic models incorporating incompressible behavior via the constraint . We show that the 'usual' homogenized integra…
Lipschitz bounds for nonuniformly elliptic integral functionals in the plane
Mathias Schäffner
We study local regularity properties of local minimizer of scalar integral functionals with controlled -growth in the two-dimensional plane. We establish Lipschitz continuit…
Local boundedness of minimizers under unbalanced Orlicz growth conditions
Andrea Cianchi, Mathias Schäffner
Local minimizers of integral functionals of the calculus of variations are analyzed under growth conditions dictated by different lower and upper bounds for the integrand. Growths…
On the Lavrentiev gap for convex, vectorial integral functionals
Lukas Koch, Matthias Ruf, Mathias Schäffner
We prove the absence of a Lavrentiev gap for vectorial integral functionals of the form $$ F: g+W_0^{1,1}(Ω)^m\to\mathbb{R}\cup\{+\infty\},\qquad F(u)=\int_ΩW(x,\mathrm{D} u)\,\mat…
New homogenization results for convex integral functionals and their Euler-Lagrange equations
Matthias Ruf, Mathias Schäffner
We study stochastic homogenization for convex integral functionals $$u\mapsto \int_D W(ω,\tfrac{x}\varepsilon,\nabla u)\,\mathrm{d}x,\quad\mbox{where}\quad u:D\subset \mathbb{R}^d\…