Related papers: Parabolic Regularity in Geometric Variational Anal…

In a recent paper the first coauthor presented a new parabolic extension (PADM) of the standard 3+1 Arnowitt, Deser, Misner formulation of the equations of general relativity. By parabolizing first-order ADM in a certain way, the PADM…

The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the lowest order time discontinuous Galerkin solution of linear parabolic equations with time-dependent…

While nowadays most gradient-based optimization methods focus on exploring the high-dimensional geometric features, the random error accumulated in a stochastic version of any algorithm implementation has not been stressed yet. In this…

The procedure to find gauge invariant variables for two-parameter nonlinear perturbations in general relativity is considered. For each order metric perturbation, we define the variable which is defined by the appropriate combination with…

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…

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…

Local regularity results are obtained for the MHD equations using as global framework the setting of parabolic Morrey spaces. Indeed, by assuming some local boundedness assumptions (in the sense of parabolic Morrey spaces) for weak…

We study the regularity of entropy solutions for quasilinear parabolic equations with anisotropic degeneracy and stochastic forcing. Building on previous works, we establish space-time regularity under a non-degeneracy condition that does…

We define here the category of partial differential equations. Special cases of morphisms from an object (equation) are symmetries of the equation and reductions of the equation by a symmetry groups, but there are many other morphisms. We…

Here, Darboux's classical results about transformations with differential substitutions for hyperbolic equations are extended to the case of parabolic equations of the form $L u = \big(D^2_{x} + a(x,y) D_x + b(x,y) D_y + c(x,y)\big)u=0$. We…

This work concerns about forward-backward multivalued stochastic systems. First of all, we prove one average principle for general stochastic differential equations in the $L^{2p}$ ($p\geq 1$) sense. Moreover, for $p=1$ a convergence rate…

A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…

This paper addresses several geometric inverse problems for some linear parabolic systems where the initial data (and sometimes also the coefficients of the equations) are unknown. The goal is to identify a subdomain within a…

In this paper we study the existence and regularity of stable manifolds associated to fixed points of parabolic type in the differentiable and analytic cases, using the parametrization method. The parametrization method relies on a suitable…

This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geometric introduction to Grobner bases. 2. An algebraic…

We solve here the so called division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that semilinear wave equations which can be written as systems involving quadratic derivative…

Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…

We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to…

Semi-Lagrangian methods have traditionally been developed in the framework of hyperbolic equations, but several extensions of the Semi-Lagrangian approach to diffusion and advection--diffusion problems have been proposed recently. These…

Classical geometric mechanics, including the study of symmetries, Lagrangian and Hamiltonian mechanics, and the Hamilton-Jacobi theory, are founded on geometric structures such as jets, symplectic and contact ones. In this paper, we shall…