Related papers: Obstacle problem for a class of parabolic equation…

We prove an existence and uniqueness result for the obstacle problem of quasilinear parabolic stochastic PDEs. The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic differential…

Existence of solutions to an obstacle $p$-Laplacian problem exhibiting a singular, discontinuous reaction is proved. The reaction term may be discontinuous in a Lebesgue-negligible set. Moreover, solutions are shown to be locally…

We prove the existence and uniqueness of solution of quasilinear stochastic partial differential equations with obstacle (OSPDEs in short) in degenerate case. Using De Giorgi's iteration, we deduce the $L^p-$estimates for the time-space…

We consider nonlinear equations having generalized Orlicz growth (also known as Musielak--Orlicz growth). We prove that if differential operators $\mathcal{A}_i$ converge locally uniformly to an operator $\mathcal{A}$, then the sequence of…

We prove the existence and uniqueness of solution of the obstacle problem for quasilinear stochastic partial differential equations (OSPDEs for short) with Neumann boundary condition. Our method is based on the analytical technics coming…

We investigate the obstacle problem for a class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional $p$-Laplacian operator with measurable coefficients. Amongst other…

This paper concerns fully nonlinear elliptic obstacle problems with oblique boundary conditions. We investigate the existence, uniqueness and $W^{2,p}$-regularity results by finding approximate non-obstacle problems with the same oblique…

We establish the existence, uniqueness, and $W^{1,2,p}$-regularity of solutions to fully-nonlinear, parabolic obstacle problems when the obstacle is the pointwise supremum of functions in $W^{1,2,p}$ and the nonlinear operator is required…

The aim of this paper is twofold: to prove, for L^1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability…

We prove Harnack's inequality for bounded weak solutions to quasilinear second order elliptic equations with generalized Orlicz growth conditions. Our approach covers new cases of variable exponent and (p,q) growth conditions.

We study the obstacle problem for the Evolutionary p-Laplace Equation when the obstacle is discontinuous and without regularity in the time variable. Two quite different procedures yield the same solution.

We consider the Cauchy problem for semilinear parabolic equation in divergence form with obstacle. We show that under natural conditions on the right-hand side of the eqution and mild conditions on the obstacle a unique continuous solution…

We consider the one and the two obstacles problems for the nonlocal nonlinear anisotropic $g$-Laplacian $\mathcal{L}_g^s$, with $0<s<1$. We prove the strict T-monotonicity of $\mathcal{L}_g^s$ and we obtain the Lewy-Stampacchia…

In this paper we study a rather wide class of quasilinear parabolic problems with nonlinear boundary condition and nonstandard growth terms. It includes the important case of equations with a $p(t,x)$-Laplacian. By means of the localization…

We prove that the spatial gradient of (variational) solutions to parabolic obstacle problems of p-Laplacian type enjoys the same regularity of the data and of the derivatives of the obstacle in the scale of Lorentz spaces.

In this paper we discuss the obstacle problem for the $p$-Laplace operator. We prove optimal growth results for the solution. Of particular interest is the point-wise regularity of the solution at free boundary points. The most surprising…

We consider the Cauchy problem for semilinear parabolic equation in divergence form with obstacle. We show that under natural conditions on the right-hand side of the equation and mild conditions on the obstacle the problem has a unique…

We study unbounded weak supersolutions of elliptic partial differential equations with generalized Orlicz (Musielak--Orlicz) growth. We show that they satisfy the weak Harnack inequality with optimal exponent provided that they belong to a…

We study the homogenization of obstacle problems in Orlicz-Sobolev spaces for a wide class of monotone operators (possibly degenerate or singular) of the $p(\cdot)$-Laplacian type. Our approach is based on the Lewy-Stampacchia inequalities,…

We consider the obstacle problem with two irregular reflecting barriers for the Cauchy-Dirichlet problem for semilinear parabolic equations with measure data. We prove the existence and uniqueness of renormalized solutions of the problem…