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Existence and relaxation results for nonlinear second order evolution inclusions

100%

Migórski S.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1995

tom 15

nr 2

129-148

In this paper we study nonlinear evolution inclusions associated with second order equations defined on an evolution triple. We prove two existence theorems for the cases where the orientor field is convex valued and nonconvex valued, respectively. We show that when the orientor field is Lipschitzean, then the set of solutions of the nonconvex problem is dense in the set of solutions of the convexified problem.

Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces

100%

Hakkarainen H., Kinnunen J., Lahti P., Lehtelä P.

Analysis and Geometry in Metric Spaces

2016

tom 4

nr 1

This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincaré inequality. Such a functional is defined via relaxation, and it defines a Radon measure on the space. For the singular part of the functional, we get the expected integral representation with respect to the variation measure. A new feature is that in the representation for the absolutely continuous part, a constant appears already in the weighted Euclidean case. As an application we show that in a variational minimization problem involving the functional, boundary values can be presented as a penalty term.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Hakkarainen H.

1 Kinnunen J.

1 Lahti P.

1 Lehtelä P.

1 Migórski S.

1 2016

1 1995

Wyniki wyszukiwania

Existence and relaxation results for nonlinear second order evolution inclusions

Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces