Related papers: Smooth approximations for fully nonlinear nonlocal…

We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial $BV$ bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal…

We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence entitled to the partial regularity result, approximating its…

We consider nonlinear, uniformly elliptic equations with random, highly oscillating coefficients satisfying a finite range of dependence. We prove that homogenization and linearization commute in the sense that the linearized equation…

In this paper we prove existence and uniqueness of viscosity solutions of elliptic systems associated to fully nonlinear operators for minimization problems that involve interconnected obstacles. This system appears, among other, in the…

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous…

We prove new borderline regularity results for solutions to fully nonlinear elliptic equations together with pointwise gradient potential estimates.

We consider the barotropic Euler equations in dimension d>1 with decaying density at spatial infinity. The phase portrait of the nonlinear ode governing the equation for spherically symmetric self-similar solutions has been introduced in…

We establish the existence of positive solutions for a nonlinear elliptic Dirichlet problem in dimension $N$ involving the $N$-Laplacian. The nonlinearity considered depends on the gradient of the unknown function and an exponential term.…

In this paper, we establish the regularity results for nonnegative viscosity solutions to fully nonlinear equations of porous medium-type in bounded domains with the zero Dirichlet boundary condition, to be precise, we prove the global…

We obtain a comparison result for solutions to nonlinear fully anisotropic elliptic problems by means of anisotropic symmetrization. As consequence we deduce a priori estimates for norms of the relevant solutions.

The existence and uniqueness of the local strong solution to the three-dimensional compressible viscoelastic fluids near the equilibrium is established. In addition to the uniform estimates on the velocity, some essential uniform estimates…

We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.

Considering the three-dimensional incompressible Navier-Stokes equations on the whole space, we address the question: is it possible to infer global regularity of a mild solution from a single approximate solution? Assuming a relatively…

We prove the convergence of meshfree collocation methods for the terminal value problems of fully nonlinear parabolic partial differential equations in the framework of viscosity solutions, provided that the basis function approximations of…

We obtain up to a flat boundary regularity results in parabolic H\"{o}lder spaces for viscosity solutions of fully nonlinear parabolic equations with oblique boundary conditions.

We consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define…

For a class of linear elliptic equations of general type with rapidly oscillating coefficients, we use the sigma-convergence method to prove the homogenization result and a corrector-type result. In the case of asymptotic periodic…

We prove the existence of a $B$-continuous viscosity solution for a class of infinite dimensional semilinear partial differential equations (PDEs) using probabilistic methods. Our approach also yields a stochastic representation formula for…

In this study, we concern the multidimensional viscosity solutions theory of a kind of semi-linear partial differential equations (PDEs). A new definition of viscosity solution for this multidimensional semi-linear PDEs which is related to…

We prove that the Navier-Stokes equation for a viscous incompressible fluid in $\mathbb{R}^d$ is locally well-posed in spaces of functions allowing spatial asymptotic expansions with log terms as $|x|\to\infty$ of any a priori given order.…