Related papers: Holomorphic Approximation and Mixed Boundary Value…
A new transform pair which can be used to solve mixed boundary value problems for Laplace's equation and the complex Helmholtz equation in bounded convex planar domains is presented. This work is an extension of Crowdy (2015, CMFT, 15,…
In the last paper \cite{R7}, it was studied Hilbert, Poincare and Neumann boundary-value problems with arbitrary measurable data for generalized analytic functions and generalized harmonic functions with applications to the relevant…
Motivated by the study of certain non linear free-boundary value problems for hyperbolic systems of partial differential equations arising in Magneto-Hydrodynamics, in this paper we show that an a priori estimate of the solution to certain…
The purpose of the present research is to investigate model mixed boundary value problems for the Helmholtz equation in a planar angular domain $\Omega_\alpha\subset\mathbb{R}^2$ of magnitude $\alpha$. The BVP is considered in a…
Using ambient space we develop a fully gauge and o(d,2) covariant approach to boundary values of AdS(d+1) gauge fields. It is applied to the study of (partially) massless fields in the bulk and (higher-order) conformal scalars, i.e.…
We consider a large class of self-adjoint elliptic problem associated with the second derivative acting on a space of vector-valued functions. We present two different approaches to the study of the associated eigenvalues problems. The…
Isoperimetric problems consist in minimizing or maximizing a cost functional subject to an integral constraint. In this work, we present two fractional isoperimetric problems where the Lagrangian depends on a combined Caputo derivative of…
The Riemann-Hilbert boundary value problem is studied for a class of planar complex vector fields $L$ in a simply connected open set $\Om\subset\R^2$. The first integrals of $L$ are used to reduce the problem into a collection of classical…
The paper is concerned with the mathematical theory and numerical approximation of systems of partial differential equations (pde) of hyperbolic, pseudo-parabolic type. Some mathematical properties of the initial-boundary-value problem…
This work presents results on the boundary properties of solutions of a complex, planar, smooth vector field $L$. Classical results in the $H^p$ theory of holomorphic functions of one variable are extended to the solutions of a class of…
We consider the spectral structure of indefinite second order boundary-value problems on graphs. A variational formulation for such boundary-value problems on graphs is given and we obtain both full and half-range completeness results. This…
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…
In this paper, we consider the boundary M of a weakly pseudoconvex domain in a Stein manifold. We point out a striking difference between the local cohomology and the global cohomology of M, and illustrate this with an example. We also…
We show that on most of the hyperbolic simply connected domains the weighted bounded rational approximation in a natural sup norm is possible only for a very sparse set of holomorphic functions (in contrast to integral approximation). The…
Recently holographic prescriptions are proposed to compute quantum complexity of a given state in the boundary theory. A specific proposal known as `holographic subregion complexity' is supposed to calculate the the complexity of a reduced…
The Guillemin boundary condition naturally appears in the study of K\"ahler geometry of toric manifolds. In the present paper, the following Guillemin boundary value problem is investigated \begin{align} \label{eq1} &\det D^2…
This paper provides results for eigencurves associated with self-adjoint linear elliptic boundary value problems. The elliptic problems are treated as a general two-parameter eigenproblem for a triple (a, b, m) of continuous symmetric…
A regular elliptic boundary-value problem over a bounded domain with a smooth boundary is studied. We prove that the operator of this problem is a Fredholm one in the two-sided refined scale of the functional Hilbert spaces and generates a…
We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with…
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…