相关论文: Nonlinear Partial Differential Equations of Ellipt…

We prove estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds. These equations are not arbitrary, but arise naturally in the study of conformal geometry.

We study inverse problems for semilinear elliptic equations with fractional power type nonlinearities. Our arguments are based on the higher order linearization method, which helps us to solve inverse problems for certain nonlinear…

It is well recognized that new types of exact travelling wave solutions to nonlinear partial differential equations can be obtained by modifications of the methods which are in hand. In this study, we extend the class of auxiliary equations…

The paper concerns singular solutions of nonlinear elliptic equations.

In this paper, we prove the partial linearization for n-dimensional nonautonomous differential equations. The conditions are formulated in terms of the dichotomy spectrum.

We provide sparse estimates for gradients of solutions to divergence form elliptic partial differential equations in terms of the source data. We give a general result of Meyers (or Gehring) type, a result for linear equations with VMO…

We study partial H\"older regularity for nonlinear elliptic systems in divergence form with double-phase growth, modeling double-phase non-Newtonian fluids in the stationary case.

In this paper, we study a broad class of fully nonlinear elliptic equations on Hermitian manifolds. On one hand, under the optimal structural assumptions we derive $C^{2,\alpha}$-estimate for solutions of the equations on closed Hermitian…

Elliptic partial differential equations (PDEs) arise in many areas of computational sciences such as computational fluid dynamics, biophysics, engineering, geophysics and more. They are difficult to solve due to their global nature and…

We prove results on solvability of nonlinear elliptic partial differential systems of principle type of second order. They are consequences of existence of non-radial solutions for nonlinear partial differential systems of Poisson type. As…

In this work, we study the existence and nonexistence of nonnegative solutions to a class of nonlocal elliptic systems set in a bounded open subset of $\mathbb{R}^N$. The diffusion operators are of type $u_i\mapsto d_i(-\Delta)^{s_i}u_i$…

We show that the knowledge of the Dirichlet-to-Neumann map on an arbitrary open portion of the boundary of a domain in $\mathbb{R}^n$, $n\ge 2$, for a class of semilinear elliptic equations, determines the nonlinearity uniquely.

This article demonstrates how variation of parameters can be successfully implemented in combination with other classical techniques, such as the method of characteristics, to derive novel classes of solutions to nonlinear partial…

In this paper, we present new techniques for solving a large variety of partial differential equations. The proposed method reduces the PDEs to first order differential equations known as classical equations such as Bernoulli, Ricatti and…

By means of a variational identity of Poho\v{z}aev-Pucci-Serrin type for solutions of class $C^1$ recently obtained, we give some necessary conditions for locating the concentration points for a class of quasi-linear elliptic problems in…

In this paper, we prove that there exists a unique solution to the Dirichlet boundary value problem for a general class of semilinear second order elliptic partial differential equations. Our approach is probabilistic. The theory of…

We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.

In this paper, we establish a global $C^2$ estimates to the Neumann problem for a class of fullly nonlinear elliptic equations. By the method of continuity, we establish the existence theorem of $k$-admissible solutions of the Neumann…

In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…

We prove the existence and uniqueness of weak solution of a Neumann boundary problem for an elliptic partial differential equation (PDE for short) with a singular divergence term which can only be understood in a weak sense. A probabilistic…