7 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…
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…
On Choquet integrals and Sobolev type inequalities
Petteri Harjulehto, Ritva Hurri-Syrjänen
We consider integrals in the sense of Choquet with respect to the -dimensional Hausdorff content for continuously differentiable functions defined on open, connected sets in th…