5 papers
Higher integrability for parabolic PDEs with generalized Orlicz growth
Peter Hästö, Jihoon Ok
We prove higher integrability of the gradient of weak solutions to nonlinear parabolic systems whose prototype is \[ \partial_t u-\mathrm{div}\Big(\frac{Ï'(z, |\nabla u|)}{|\nabla…
Intrinsic Schauder estimates at nearly linear growth
Cristiana De Filippis, Filomena De Filippis, Peter Hästö
We develop a nonlinear potential theoretic framework for Schauder estimates for vector-valued solutions of a broad class of nonautonomous variational problems at nearly linear grow…
Mean oscillation conditions for nonlinear equation and regularity results
Peter Hästö, Mikyoung Lee, Jihoon Ok
We consider general nonlinear elliptic equations of the form \[ \operatorname{div}\, A(x,Du) = 0 \quad \text{in } Ω, \] where satisfies a…
Relaxation of quasi-convex functionals with variable exponent growth
Giacomo Bertazzoni, Petteri Harjulehto, Peter Hästö +1
We prove a relaxation result for a quasi-convex bulk integral functional with variable exponent growth in a suitable space of bounded variation type. A key tool is a decomposition…
Monotone approximation of differentiable convex functions with applications to general minimization problems
Petteri Harjulehto, Peter Hästö, Andrea Torricelli
We study minimizers of non-autonomous energies with minimal growth and coercivity assumptions on the energy. We show that the minimizer is nevertheless the solution of the relevant…