7 results match your criteria Calculus Of Variations And Partial Differential Equations[Journal]

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On the geometry of geodesics in discrete optimal transport.

Calc Var Partial Differ Equ 2019 11;58(1):19. Epub 2018 Dec 11.

3Institute of Mathematics, Friedrich Schiller University Jena, 07737 Jena, Germany.

We consider the space of probability measures on a discrete set , endowed with a dynamical optimal transport metric. Given two probability measures supported in a subset , it is natural to ask whether they can be connected by a constant speed geodesic with support in at all times. Our main result answers this question affirmatively, under a suitable geometric condition on introduced in this paper. Read More

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http://dx.doi.org/10.1007/s00526-018-1456-1DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6390900PMC
December 2018

Ground states in the diffusion-dominated regime.

Calc Var Partial Differ Equ 2018 11;57(5):127. Epub 2018 Aug 11.

4Dipartimento di Ingegneria, Università degli Studi di Napoli "Parthenope", 80143 Naples, Italy.

We consider macroscopic descriptions of particles where repulsion is modelled by non-linear power-law diffusion and attraction by a homogeneous singular kernel leading to variants of the Keller-Segel model of chemotaxis. We analyse the regime in which diffusive forces are stronger than attraction between particles, known as the diffusion-dominated regime, and show that all stationary states of the system are radially symmetric non-increasing and compactly supported. The model can be formulated as a gradient flow of a free energy functional for which the overall convexity properties are not known. Read More

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http://link.springer.com/10.1007/s00526-018-1402-2
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http://dx.doi.org/10.1007/s00526-018-1402-2DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6190998PMC
August 2018
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Global existence of Dirac-wave maps with curvature term on expanding spacetimes.

Calc Var Partial Differ Equ 2018 20;57(5):119. Epub 2018 Jul 20.

2Department of Mathematics, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany.

We prove the global existence of Dirac-wave maps with curvature term with small initial data on globally hyperbolic manifolds of arbitrary dimension which satisfy a suitable growth condition. In addition, we also prove a global existence result for wave maps under similar assumptions. Read More

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http://dx.doi.org/10.1007/s00526-018-1389-8DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6190925PMC

Quasi-periodic two-scale homogenisation and effective spatial dispersion in high-contrast media.

Authors:
Shane Cooper

Calc Var Partial Differ Equ 2018 27;57(3):76. Epub 2018 Apr 27.

Department of Mathematical Sciences, Durham University, Lower Mountjoy, Durham, DH1 3LE UK.

The convergence of spectra via two-scale convergence for double-porosity models is well known. A crucial assumption in these works is that the stiff component of the body forms a connected set. We show that under a relaxation of this assumption the (periodic) two-scale limit of the operator is insufficient to capture the full asymptotic spectral properties of high-contrast periodic media. Read More

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http://dx.doi.org/10.1007/s00526-018-1365-3DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6435209PMC

Horizontal curves of hyperbolic metrics.

Calc Var Partial Differ Equ 2018 15;57(4):106. Epub 2018 Jun 15.

2Mathematics Institute, University of Warwick, Coventry, CV4 7AL UK.

We analyse the fine convergence properties of one parameter families of hyperbolic metrics that move always in a horizontal direction, i.e. orthogonal to the action of diffeomorphisms. Read More

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http://dx.doi.org/10.1007/s00526-018-1386-yDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6432971PMC

Minkowski valuations on convex functions.

Calc Var Partial Differ Equ 2017 23;56(6):162. Epub 2017 Oct 23.

Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/1046, 1040 Wien, Austria.

A classification of [Formula: see text] contravariant Minkowski valuations on convex functions and a characterization of the projection body operator are established. The associated LYZ measure is characterized. In addition, a new [Formula: see text] covariant Minkowski valuation on convex functions is defined and characterized. Read More

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http://dx.doi.org/10.1007/s00526-017-1243-4DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5653878PMC
October 2017
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On the structure of solutions to a class of quasilinear elliptic Neumann problems. Part II.

Authors:
Chunshan Zhao Yi Li

Calc Var Partial Differ Equ 2005 May;212(1):208-233

Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA.

We continue our work (Y. Li, C. Zhao in J Differ Equ 212:208-233, 2005) to study the structure of positive solutions to the equation epsilon(m) Delta(m)u - u(m-1) + f(u) = 0 with homogeneous Neumann boundary condition in a smooth bounded domain of RN (N >/= 2). Read More

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http://dx.doi.org/10.1016/j.jde.2004.07.021DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2917850PMC
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