We consider the Dirichlet-to-Neumann map associated to the Schrö– dinger equation with a potential on a bounded domain Ω ⊂ Rn, n ≥ 3. We show that the integral of the potential over a two-plane Π is determined by the values of the integral kernel of the Dirichlet-to-Neumann map on any open subset U ⊂ ∂Ω which contains Π ∩ ∂Ω. 0 Introduction For Ω a bounded domain in R with Lipschitz boundary, ∂...

The L-theory of solutions of the homogeneous A-harmonic equation d A x, dω 0 for differential forms has been very well developed in recent years. Many L-norm estimates and inequalities, including the Hardy-Littlewood inequalities, Poincaré inequalities, Caccioppoli-type estimates, and Sobolev imbedding inequalities, for solutions of the homogeneous A-harmonic equation have been established; see...

The modified Maxwell’s Steklov eigenvalue problem is a new arising from the study of inverse electromagnetic scattering problems. In this paper, we investigate two finite element methods for and perform convergence analysis. Moreover, monotonic discrete eigenvalues computed by one analyzed.

In this paper, we study the upper bounds for discrete Steklov eigenvalues on trees via geometric quantities. For a finite tree, prove sharp first nonzero eigenvalue by reciprocal of size boundary and diameter respectively. We also similar estimates higher order eigenvalues.

We analyze the decomposition of the enveloping algebra of the conformal algebra in arbitrary dimension with respect to the mass-squared operator. It emerges that the subalgebra that commutes with the mass-squared is generated by its Poincaré subalgebra together with a vector operator. The special cases of the conformal algebras of two and three dimensions are described in detail, including the ...

A new approach to hyperbolic inverse problems. Abstract We present a modification of the BC-method in the inverse hyper-bolic problems. The main novelty is the study of the restrictions of the solutions to the characteristic surfaces instead of the fixed time hyperplanes. The main result is that the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely deter...

Let H be a Hopf algebra and let B be a Koszul H-module algebra. We provide necessary and sufficient conditions for a filtered algebra to be a Poincaré-Birkhoff-Witt (PBW) deformation of the smash product algebra B#H. Many examples of these deformations are given.

In this paper, following Nachman’s idea [14] and Haberman and Tataru’s idea [9], we reconstruct C conductivity γ or Lipchitz conductivity γ with small enough value of |∇logγ| in a Lipschitz domain Ω from the Dirichlet-to-Neumann map Λγ . In the appendix the authors and R. M. Brown recover the gradient of a C-conductivity at the boundary of a Lipschitz domain from the Dirichlet-to-Neumann map Λγ...

Abstract. As the classical (p, q)-Poincaré inequality is known to fail for 0 < p < 1, we introduce the notion of weighted multilinear Poincaré inequality as a natural alternative when m-fold products and 1/m < p are considered. We prove such weighted multilinear Poincaré inequalities in the subelliptic context associated to vector fields of Hörmader type. We do so by establishing multilinear re...

We prove Reilly-type upper bounds for the first non-zero eigen-value of Steklov problem associated with p-Laplace operator on sub-manifolds boundary Euclidean spaces as well Riemannian products R × M where is a complete manifold.