相关论文: Investigation of solutions of boundary value probl…

We develop an elliptic theory based in $L^2$ of boundary value problems for general wedge differential operators of first order under only mild assumptions on the boundary spectrum. In particular, we do not require the indicial roots to be…

We consider first-order elliptic differential operators acting on vector bundles over smooth manifolds with smooth boundary, which is permitted to be noncompact. Under very mild assumptions, we obtain a regularity theory for sections in the…

A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…

Given any elliptic system with $t$-independent coefficients in the upper-half space, we obtain representation and trace for the conormal gradient of solutions in the natural classes for the boundary value problems of Dirichlet and Neumann…

We investigate existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the…

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…

We investigate regular elliptic boundary-value problems in bounded domains and show the Fredholm property for the related operators in an extended scale formed by inner product Sobolev spaces (of arbitrary real orders) and corresponding…

In present paper we study a boundary value problem for a mixed parabolic-hyperbolic type equation in a rectangular domain and prove the existence of unique solution of this problem. In theory of boundary value problems for second order…

We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…

In 2002, J.M.Rassias (Uniqueness of quasi-regular solutions for bi-parabolic elliptic bi-hyperbolic Tricomi problem, Complex Variables, 47 (8) (2002), 707-718) imposed and investigated the bi-parabolic elliptic bi-hyperbolic mixed type…

This paper presents high-order numerical methods for solving boundary value problems associated with the Lane-Emden equation, which frequently arises in astrophysics and various nonlinear models. A major challenge in studying this equation…

This paper offers a number of examples showing that in the case of two independent variables the uniform ellipticity of a linear system of differential equations with partial derivatives of the second order, which fulfills condition (3), do…

The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with three singular coefficients, which could be expressed in terms of a confluent hypergeometric function…

We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded…

Boundary value problems for second-order elliptic equations in divergence form, whose nonlinearity is governed by a convex function of non-necessarily power type, are considered. The global boundedness of their solutions is established…

The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…

In the first part of the article, we give necessary and sufficient conditions for the solvability of a class of nonlinear elliptic boundary value problems with nonlinear boundary conditions involving the q-Laplace-Beltrami operator. In the…

The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract…

Recursively compressed inverse preconditioning (RCIP) is a kernel-independent and purely numerical method for solving Fredholm second kind boundary integral equations in situations where the boundary shape induces a non-smooth behavior in…

We prove the Fredholm alternative for a class of two-dimensional first-order hyperbolic systems with periodic-Dirichlet boundary conditions. Our approach is based on a regularization via a right parametrix.