9 papers
A note on new mapping properties for Wolff potential
Petteri Harjulehto, Ritva Hurri-Syrjänen
We study integrability properties of the Wolff potential in context of Choquet integrals with respect to the Hausdorff content. As an application we give integrability results to t…
A note on Sobolev inequalities in the lower limit case
Petteri Harjulehto, Ritva Hurri-Syrjänen
We study Poincare-Sobolev type inequalities for compactly supported smooth functions which are defined in the Euclidean -space and whose absolute value of gradient are Choquet $…
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…
On Lebesgue points and measurability with Choquet integrals
Petteri Harjulehto, Ritva Hurri-Syrjänen
We consider Choquet integrals with respect to dyadic Hausdorff content of non-negative functions which are not necessarily Lebesgue measurable. We study the theory of Lebesgue poin…
On Choquet integrals and pointwise estimates
Petteri Harjulehto, Ritva Hurri-Syrjänen
We consider inequalities where integrals are defined in the sense of Choquet with respect to Hausdorff content. We study cases where continuously differentiable functions are defin…
Stability of solutions to obstacle problems with generalized Orlicz growth
Petteri Harjulehto, Arttu Karppinen
We consider nonlinear equations having generalized Orlicz growth (also known as Musielak--Orlicz growth). We prove that if differential operators converge locally u…