We investigate which elliptic PDEs have the property that every viscosity supersolution belongs to a Sobolev space $$W^{1,q}_{loc}(\Omega )$$ , $$\Omega \subseteq \mathbb {R}^n$$ . The asymptotic cone of operator’s sublevel set seems be essential. It turns out much can said if we know how is related dominative p-Laplacian, with $$p = \frac{n-1}{n}q + 1$$ show that, in certain sense, this minima...

We formulate a robust optimal stopping-time problem for a state-space system and give the connection between various notions of lower value function for the associated games (and storage function for the associated dissipative system) with solutions of the appropriate variational inequality (VI) (the analogue of the HamiltonJacobi-Bellman-Isaacs equation for this setting). We show that the stop...

We study the superhedging problem for American options with completely irregular payoffs in a non-linear and incomplete market model default. give dual representation of seller’s (superhedging) price terms value mixed control/stopping problem, involving suitable set equivalent probability measures. characterize process as minimal supersolution two types reflected BSDEs: constrained one an optio...

We study existence of solutions for a boundary degenerate (or singular) quasilinear equation in smooth bounded domain under Dirichlet conditions. consider weighted p-Laplacian operator with coefficient that is locally inside the and satisfying certain additional integrability assumptions. Our main result applies value problems involving continuous non-linearities having no growth restriction, b...

In the present paper we deal with a quasilinear problem involving singular term and parametric superlinear perturbation. We are interested in existence, nonexistence multiplicity of positive solutions as parameter λ > 0 ...