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math.AP2025
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{φ'(z, |\nabla u|)}{|\nabla…
math.AP2025
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…
math.AP2025
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 qu…