3 papers
math.AP2025
Regularity for monotone Operators and applications to homogenization of -Laplace type equations
Lukas Koch, Mathias Schäffner, 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…
math.AP2024
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)\,\m…
math.AP2024
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…