Variational fractals
Approximation of the solutions of some variational inequalities
Analysis and Numerics of Some Fractal Boundary Value Problems
We describe some recent results for boundary value problems with fractal boundaries. Our aim is to show that the numerical approach to boundary value problems, so much cherished and in many ways pioneering developed by Enrico Magenes, takes on a special relevance in the theory of boundary value problems in fractal domains and with fractal operators. In this theory, in fact, the discrete numerical analysis of the problem precedes the, and indeed give rise to, the asymptotic continuous problem, reverting...
Variational Inequalities with One-Sided Irregular Obstacles.
Irregular obstacles and quasi-variational inequalities of stochastic impulse control
Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces
We prove local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type. Our results apply to some general classes of selfadjoint subelliptic operators as well as to Dirichlet operators on certain self-similar fractals, like the Sierpinski gasket. We also define intrinsic BV spaces and perimeters and prove related isoperimetric inequalities.
Wiener criterion for degenerate elliptic obstacle problem
We give a Wiener criterion for the continuity of an obstacle problem relative to an elliptic degenerate problem with a weight in the class.
Wiener criterion for degenerate elliptic obstacle problem
We give a Wiener criterion for the continuity of an obstacle problem relative to an elliptic degenerate problem with a weight in the class.
Non linear quasi variational inequalities and stochastic impulse control theory
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