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In this paper, we study evolutive Hamilton Jacobi equations with Hamiltonians that are discontinuous in time, posed on a simple network consisting of two edges on the real line connected at a single junction. We introduce a notion of…
In this paper, we consider a family of Jacobi-type algorithms for simultaneous orthogonal diagonalization problem of symmetric tensors. For the Jacobi-based algorithm of [SIAM J. Matrix Anal. Appl., 2(34):651--672, 2013], we prove its…
The quantization method based on the quantum Hamiltonian Jacobi equation, is extended to two-dimensional non-separable but integrable Hamiltonians. It is shown that each wave function for those systems corresponds to a well-defined family…
The classical problem of algebraic models for homotopy types is precisely stated, to our knowledge for the first time. Two different natural statements for this problem are produced, the simplest one being entirely solved by the notion of…
We study the Lie point symmetries of Einstein's equations for the Friedmann-Roberstson-Walker Cosmology. They form either a two - dimensional or a three - dimensional solvable group depending on the form of the self interacting potential.…
Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…
We prove the existence and uniqueness up to translations of the solution to a Minkowski type problem for the torsional rigidity in the class of open bounded convex subsets of the $n$-dimensional Euclidean space. For the existence part we…
For a large class of time-dependent non-Hermitain Hamiltonians expressed in terms linear and bilinear combinations of the generators for an Euclidean Lie-algebra respecting different types of PT-symmetries, we find explicit solutions to the…
This paper focuses on the analysis of conforming virtual element methods for general second-order linear elliptic problems with rough source terms and applies it to a Poisson inverse source problem with rough measurements. For the forward…
This paper studies the existence and uniqueness of a classical solution to a type of Robin boundary problems on the nonnegative orthant. We propose a new decomposition-homogenization method for the Robin boundary problem based on…
In this work we show how to complete some Hamilton-Jacobi solutions of linear, nonconservative classical oscillatory systems which appeared in the literature and we extend these complete solutions to the quantum mechanical case. In…
We study existence and non-existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all critical points of the Hilbert-Einstein functional…
An algorithm recently presented by Lake to obtain all static spherically symmetric perfect fluid solutions, is extended to the case of locally anisotropic fluids (principal stresses unequal). As expected, the new formalism requires the…
We clarify how close a second order fully nonlinear equation can come to uniform ellipticity, through counting large eigenvalues of the linearized operator. This suggests an effective and novel way to understand the structure of fully…
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical…
We study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the…
This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes…
A method to construct trihamiltonian extensions of a separable system is presented. The procedure is tested for systems, with a natural Hamiltonian, separable in classical sense in one of the four orthogonal separable coordinate systems of…
The three-particle Hamiltonian obtained by replacing the two-body trigonometric potential of the Sutherland problem by a three-body one of a similar form is shown to be exactly solvable. When written in appropriate variables, its…
In this work, we study the super-Liouville equation on the sphere with positive coefficient functions. We first examine the behavior of the equation under conformal transformations and derive a Pohozaev-type identity, which generalizes the…