Related papers: Solution of the dbar-Neumann problem on a bi-disc
We establish uniqueness for sign-changing solutions to Trudinger's parabolic equation with time dependent $C^2$ Dirichlet boundary data.
We examine $(D-2)$-brane solutions in supergravities, showing that they fall into four categories depending on the details of the dilaton coupling. In general they describe domain walls, although in one of the four categories the metric…
We continue the program initiated in a previous work, of applying integro-differential methods to Neumann Homogenization problems. We target the case of linear periodic equations with a singular drift, which includes (with some regularity…
We consider the equation $-\Delta u= |x|^{\alpha}|u|^{p-1}u$ for any $\alpha\geq 0$, either in $\mathbb R^2$ or in the unit ball $B$ of $\mathbb R^2$ centered at the origin with Dirichlet or Neumann boundary conditions. We give a sharp…
We prove several results for the Dirichlet, Neumann and Regularity problems for the Laplace equation in graph Lipschitz domains in the plane, considering $A_{\infty}$-measures on the boundary. More specifically, we study the…
Let D be a domain in the quaternionic space H. We prove a differential criterion that characterizes Fueter-regular quaternionic functions f:bD -> H of class C^1. We find differential operators T and N, with complex coefficients, such that a…
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 completion problem to recover a rational matrix function which is j-unitary on the line is treated. A Dirac type system with singularities on the semiaxis is recovered explicitly by its left reflection coefficient. The close connection…
We consider inverse boundary value problems for elliptic equations of second order of determining coefficients by Dirichlet-to-Neumann map on subboundaries, that is, the mapping from Dirichlet data supported on $\partial\Omega\setminus…
This study is devoted to proving the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary data. The problem is driven by a discontinuous power nonlinearity and a nonsmooth prescribed data. Additionally, we…
In this article, we obtain existence and uniqueness results to some problems involving complex nonlinear fractional differential equations (FDEs) in the closed unit disc of C. By help of these results, we prove that some IVPs for some…
Global existence for weak solutions to systems of nematic liquid crystals, with non-constant fluid density has been established by several authors. In this paper, we establish the regularity and uniqueness results for solutions to the…
We address the open problem of existence of singularities for the complex Ginzburg-Landau equation. Using a combination of rigourous results and numerical computations, we describe a countable family of self-similar singularities. Our…
We prove continuity for bounded weak solutions of a nonlinear nonlocal parabolic type equation associated to a Dirichlet form with a rough kernel. The equation is allowed to be singular at the level zero, and solutions may change sign. If…
We analyze dispersion relations of the equations recently proposed by Ahluwalia for describing neutrino. Equations for type-II spinors are deduced on the basis of the Wigner rules for left- and right- 2-spinors and the Ryder-Burgard…
This paper examines the behavior of a positive solution $u\in C^{1,\alpha}(\Bar{\Omega})$ of the $(p,q)$ Laplace equation with a singular term and zero Dirichlet boundary condition. Specifically, we consider the equation: \begin{equation*}…
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.
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
A family of nonlinear partial differential equations of divergence form is considered. Each one is the Euler-Lagrange equation of a natural Riemaniann variational problem of geometric interest. New uniqueness results for the entire…
For a stationary and axisymmetric spacetime, the vacuum Einstein field equations reduce to a single nonlinear PDE in two dimensions called the Ernst equation. By solving this equation with a {\it Dirichlet} boundary condition imposed along…