Related papers: Recent progress in the Calderon problem with parti…
We consider three generalizations of the isoperimetric problem to higher codimension and provide results on equilibrium, stability, and minimization.
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
We consider the problem of recovering the coefficient \sigma(x) of the elliptic equation \grad \cdot(\sigma \grad u)=0 in a body from measurements of the Cauchy data on possibly very small subsets of its surface. We give a constructive…
I review recent developments in numerical relativity, focussing on progress made in 3D black hole evolution. Progress in development of black hole initial data, apparent horizon boundary conditions, adaptive mesh refinement, and…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…
We present a brief review of some recent results on conformal anomalies in four and more dimensions. The discussion is intended for relativists, so some background on the quantum origin of anomalies and of their simple properties in D=2 is…
Two related issues are discussed, which might be easily explored by present and future COMPASS experiments. The first one deals with the new world of transversity, the fundamental polarized parton distribution so far totally unknown. The…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
This paper is concerned with the forward and inverse problems for the fractional semilinear elliptic equation $(-\Delta)^s u +a(x,u)=0$ for $0<s<1$. For the forward problem, we proved the problem is well-posed and has a unique solution for…
The aim of this paper is to report on recent development on the conformal fractional Laplacian, both from the analytic and geometric points of view, but especially towards the PDE community.
Uniqueness and reconstruction in the three-dimensional Calder\'on inverse conductivity problem can be reduced to the study of the inverse boundary problem for Schr\"odinger operators $-\Delta +q $. We study the Born approximation of $q$ in…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
A concise analytical formula is developed for the inverse of an invertible 3 x 3 matrix using a telescoping method, and is generalized to larger square matrices. The formula is confirmed using randomly generated matrices in Matlab
We recall the physical features of the parton distributions in the quantum statistical approach of the nucleon. Some predictions from a next-to-leading order QCD analysis are compared to recent experimental results. We also consider their…
We discuss the phenomenological and theoretical implications of recent progresses in the evaluation of multi-Pomeron vertices in high-energy perturbative QCD.
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…
Spingarn's method of partial inverses has found many applications in nonlinear analysis and in optimization. We show that it can be employed to solve composite monotone inclusions in duality, thus opening a new range of applications for the…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…