Related papers: Unique continuation for fully nonlinear elliptic e…

In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order…

This paper aims to investigate a Harnack inequality for non-negative solutions of the normalized infinity Laplacian with nonlinear absorption and gradient terms. More specifically, we establish a Harnack inequality for non-negative…

In this work we establish local $C^{2,\alpha}$ regularity estimates for flat solutions to non-convex fully nonlinear elliptic equations provided the coefficients and the source function are of class $C^{0,\alpha}$. For problems with merely…

We show that for any uniformly elliptic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term one can find an approximating equation which has a unique continuous and having the second…

In this paper, we prove two unique continuation results for second order elliptic equations with Robin boundary conditions on $C^{1,1}$ domains. The first one is a sharp vanishing order estimate of Robin problems with Lipschitz coefficients…

We consider radial solutions of a general elliptic equation involving a weighted Laplace operator. We establish the uniqueness of the radial bound state solutions to $$ {div}\big(\mathsf A\,\nabla v\big)+\mathsf…

We introduce a notion of viscosity solutions for a general class of elliptic-parabolic phase transition problems. These include the Richards equation, which is a classical model in filtration theory. Existence and uniqueness results are…

We prove an existence and uniqueness result for solutions to linear $X$-elliptic equations with $L^1$ data and zero Dirichlet boundary conditions. Such solutions depend continuously on the datum. Moreover, we show that an improvement in the…

We establish convergence as the viscosity vanishes of solutions of the Navier-Stokes equations to a solution of the Euler equations for inflow, outflow boundary conditions. We extend the approach of Temam and Wang 2002, allowing the…

This paper introduces a notion of regularity (or irregularity) of the point at infinity for the unbounded open subset of $\rr^{N}$ concerning second order uniformly elliptic equations with bounded and measurable coefficients, according as…

Our principal object of study is the modulus of continuity of a periodic or uniformly vanishing function \( u: \mathbb{R} ^{n} \rightarrow \mathbb{R} \) which satisfies a degenerate elliptic equation \( F(x, u, \nabla u, D^{2} u) = 0 \) in…

We provide the Alexandroff-Bakelman-Pucci estimate and global $C^{1, \alpha}$-regularity for a class of singular/degenerate fully nonlinear elliptic equations. We also derive the existence of a viscosity solution to the Dirichlet problem…

We establish the vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for three-dimensional compressible isentropic flow in the whole space. It is shown that there exists a unique regular solution of compressible…

$(-1)$-homogeneous axisymmetric no-swirl solutions of three dimensional incompressible stationary Navier-Stokes equations which are smooth on the unit sphere minus the north and south poles have been classified, %as a four parameter family…

We establish near-optimal quantitative uniqueness of continuation for solutions of evolution equations vanishing on the lateral boundary. These results were obtained simply by combining existing observability inequalities and energy…

In this paper, we establish pointwise boundary ${{C}^{1,\alpha}}$ estimates for viscosity solutions of some degenerate fully nonlinear elliptic equations on ${C^{1,\alpha}}$ domains. Instead of straightening out the boundary, we utilize the…

We study whether the solutions of a fully nonlinear, uniformly parabolic equation with superquadratic growth in the gradient satisfy initial and homogeneous boundary conditions in the classical sense, a problem we refer to as the classical…

We study Hessian fully nonlinear uniformly elliptic equations and show that the second derivatives of viscosity solutions of those equations (in 12 or more dimensions) can blow up in an interior point of the domain. We prove that the…

We present a new stability result for viscosity solutions of fully nonlinear parabolic equations which allows to pass to the limit when one has only weak convergence in time of the nonlinearities.

We consider the vanishing viscosity limit of the Navier-Stokes equations in a half space, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes…