相关论文: Second-Order Elliptic Integro-Differential Equatio…

A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth…

This paper introduces a convenient solution space for the uniformly elliptic fully nonlinear path dependent PDEs. It provides a wellposedness result under standard Lipschitz-type assumptions on the nonlinearity and an additional assumption…

We derive a priori second order estimates for solutions of a class of fully nonlinear elliptic equations on Riemannian manifolds under some very general structure conditions. We treat both equations on closed manifolds, and the Dirichlet…

This review is devoted to the large-scale rheology of suspensions of rigid particles in Stokes fluid. After describing recent results on the definition of the effective viscosity of such systems in the framework of homogenization theory, we…

Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized…

In this paper the concept of measure of noncompactness is applied to prove the existence of solution for a boundary value problem for an infinite system of second order differential equations in $\ell_{p}$ space. We change the boundary…

We establish a superposition principle in disjoint variables for the inhomogeneous infinity-Laplace equation. We show that the sum of viscosity solutions of the inhomogeneous infinity-Laplace equation in separate domains is a viscosity…

In this paper, we propose two parallel extragradient - viscosity methods for finding a particular element in the common solution set of a system of equilibrium problems and finitely many fixed point problems. This particular point is the…

In this work we introduce a viscosity-based notion of solution for general approximation schemes associated with partial differential equations, such as dynamic programming principles~(DPPs). A key feature of our approach is that it…

This paper is concerned with developing accurate and efficient numerical methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in multiple spatial dimensions. It presents a general framework…

As explained in detail in the prologue to this manuscript, boundedness of weak solutions for general classes of elliptic equations in divergence form is a classic tool for achieving higher regularity. We propose here some global boundedness…

We establish new results for path-dependent Hamilton-Jacobi equations with nonlinear monotone, and coercive operators on Hilbert space, which were initially studied in Bayraktar and Keller [J. Funct. Anal., 275 (8) (2018), pp. 2096-2161].…

In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successfully obtain a class of drifting solutions with elliptic…

In this work, we suggest a general viscosity implicit midpoint rule for nonexpansive mapping in the framework of Hilbert space. Further, under the certain conditions imposed on the sequence of parameters, strong convergence theorem is…

This is a truncated version of the paper "Degenerate diffusion with a drift potential: a viscosity solutions approach", co-authored with I. C. Kim. The purpose of this version is to withdraw the claim of quantitative rate of convergence of…

We study the problem of coupling Einstein's equations to a relativistic and physically well-motivated version of the Navier-Stokes equations. Under a natural evolution condition for the vorticity, we prove existence and uniqueness in a…

Qualitative properties of a second order elliptic equation from the anisotropic elasticity are investigated. Some explicit solutions for a disk are presented. Behaviour of these solutions in dependence of coefficients is investigated. The…

We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range amongst those with unbalanced…

In this paper, we mainly establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for a class of fully nonlinear second-order elliptic equations related to the eigenvalues of the Hessian, with…

We give a simple proof of the strong maximum principle for viscosity subsolutions of fully nonlinear elliptic PDEs on the form $$ F(x,u,Du,D^2u) = 0 $$ under suitable structure conditions on the equation allowing for non-Lipschitz growth in…