Entropy Solution Theory for Fractional Degenerate Convection-Diffusion Equations [PDF]
, 2010 We study a class of degenerate convection diffusion equations with a fractional nonlinear diffusion term. These equations are natural generalizations of anomalous diffusion equations, fractional conservations laws, local convection diffusion equations ...
Alibaud +38 more
core +2 more sources
Cauchy's functional equation and extensions: Goldie's equation and inequality, the Go{\l}\k{a}b-Schinzel equation and Beurling's equation [PDF]
, 2014 The Cauchy functional equation is not only the most important single functional equation, it is also central to regular variation. Classical Karamata regular variation involves a functional equation and inequality due to Goldie; we study this, and its ...
Bingham, N. H., Ostaszewski, A. J.
core +2 more sources
Global minimizers for axisymmetric multiphase membranes [PDF]
, 2012 We consider a Canham-Helfrich-type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes.
Choksi, Rustum +2 more
core +6 more sources
Mixed spatially varying $L^2$-BV regularization of inverse ill-posed problems [PDF]
, 2014 Several generalizations of the traditional Tikhonov-Phillips regularization method have been proposed during the last two decades. Many of these generalizations are based upon inducing stability throughout the use of different penalizers which allow the ...
Mazzieri, Gisela L. +2 more
core +2 more sources
Higher-dimensional generalizations of the Berry curvature [PDF]
, 2020 A family of finite-dimensional quantum systems with a nondegenerate ground state gives rise to a closed two-form on the parameter space, the curvature of the Berry connection.
Kapustin, Anton, Spodyneiko, Lev
core +2 more sources
A direct approach to the stable distributions [PDF]
, 2016 The explicit form for the characteristic function of a stable distribution on the line is derived analytically by solving the associated functional equation and applying theory of regular variation, without appeal to the general L\'evy-Khintchine ...
Pitman, E. J. G., Pitman, Jim
core +1 more source
Functional Meyer-Tanaka Formula
, 2017 The functional Ito formula, firstly introduced by Bruno Dupire for continuous semimartingales, might be extended in two directions: different dynamics for the underlying process and/or weaker assumptions on the regularity of the functional. In this paper,
Saporito, Yuri F.
core +1 more source
Existence of minimizers for the $2$d stationary Griffith fracture model [PDF]
, 2016 We consider the variational formulation of the Griffith fracture model in two spatial dimensions and prove existence of strong minimizers, that is deformation fields which are continuously differentiable outside a closed jump set and which minimize the ...
Conti, Sergio +2 more
core +3 more sources
Finite Rank Bargmann-Toeplitz Operators with Non-Compactly Supported Symbols [PDF]
, 2012 Theorems about characterization of finite rank Toeplitz operators in Fock-Segal-Bargmann spaces, known previously only for symbols with compact support, are carried over to symbols without that restriction, however with a rather rapid decay at infinity ...
Rozenblum, Grigori
core +2 more sources
Nondifferentiable functions of one-dimensional semimartingales
, 2010 We consider decompositions of processes of the form $Y=f(t,X_t)$ where $X$ is a semimartingale. The function $f$ is not required to be differentiable, so It\^{o}'s lemma does not apply.
Lowther, George
core +1 more source