University of Jyväskylä | JYX Digital Repository

  • English  | Give feedback |
    • suomi
    • English
 
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
View Item 
  • JYX
  • Artikkelit
  • Matemaattis-luonnontieteellinen tiedekunta
  • View Item
JYX > Artikkelit > Matemaattis-luonnontieteellinen tiedekunta > View Item

Everywhere differentiability of viscosity solutions to a class of Aronsson's equations

ThumbnailFinal Draft
View/Open
380.6 Kb

Downloads:  
Show download detailsHide download details  
Siljander, J., Wang, C., & Zhou, Y. (2017). Everywhere differentiability of viscosity solutions to a class of Aronsson's equations. Annales de l'Institut Henri Poincare (C). Analyse non Lineaire, 34(1), 119-138. https://doi.org/10.1016/j.anihpc.2015.10.003
Published in
Annales de l'Institut Henri Poincare (C). Analyse non Lineaire
Authors
Siljander, Juhana |
Wang, Changyou |
Zhou, Yuan
Date
2017
Discipline
MatematiikkaMathematics
Copyright
© 2015 Elsevier Masson SAS. This is a final draft version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.

 
We show the everywhere differentiability of viscosity solutions to a class of Aronsson equations in R n for n ≥ 2, where the coefficient matrices A are assumed to be uniformly elliptic and C 1,1 . Our result extends an earlier important theorem by Evans and Smart [19] who have studied the case A = In which correspond to the ∞-Laplace equation. We also show that every point is a Lebesgue point for the gradient. In the process of proving the results we improve some of the gradient estimates obtained for the infinity harmonic functions. The lack of suitable gradient estimates has been a major obstacle for solving the C 1,α problem in this setting, and we aim to take a step towards better understanding of this problem, too. A key tool in our approach is to study the problem in a suitable intrinsic geometry induced by the coefficient matrix A. Heuristically, this corresponds to considering the question on a Riemannian manifold whose the metric is given by the matrix A.
Publisher
Elsevier Masson
ISSN Search the Publication Forum
0294-1449
Keywords
L∞-variational problem absolute minimizer everywhere differentiability Aronsson's equation
DOI
https://doi.org/10.1016/j.anihpc.2015.10.003
URI

http://urn.fi/URN:NBN:fi:jyu-201701101123

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/25279683

Metadata
Show full item record
Collections
  • Matemaattis-luonnontieteellinen tiedekunta [4544]

Related items

Showing items with similar title or keywords.

  • Sharpness of the differentiability almost everywhere and capacitary estimates for Sobolev mappings 

    Hencl, Stanislav; Tengvall, Ville (European Mathematical Society Publishing House; Real Sociedad Matematica Espanola, 2017)
    We give sharp conformal conditions for the dfferentiability in the Sobolev space W1, n-1 loc (Ω,Rn). Furthermore, we show that the space W1, n-1 loc (Ω,Rn) can be considered as the borderline space for some capacitary ...
  • On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems 

    Matculevich, Svetlana; Wolfmayr, Monika (Elsevier, 2018)
    This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker–Planck problem appearing in computational neuroscience. ...
  • L2-variation of Lévy driven BSDEs with non-smooth terminal conditions 

    Geiss, Christel; Steinicke, Alexander (International Statistical Institute; Bernoulli Society for Mathematical Statistics and Probability, 2016)
    We consider the L2-regularity of solutions to backward stochastic differential equations (BSDEs) with Lipschitz generators driven by a Brownian motion and a Poisson random measure associated with a Lévy process (Xt)t∈[0,T]. ...
  • Decoupling on the Wiener space and variational estimates for BSDEs 

    Ylinen, Juha (University of Jyväskylä, 2015)
  • Uniqueness of positive solutions to some Nonlinear Neumann Problems 

    Wan, Youyan; Xiang, Changlin (Academic Press, 2017)
    Using the moving plane method, we obtain a Liouville type theorem for nonnegative solutions of the Neumann problem ⎧ ⎨ ⎩ div (ya∇u(x, y)) = 0, x ∈ Rn,y > 0, lim y→0+yauy(x, y) = −f(u(x, 0)), x ∈ Rn, under general ...
  • Browse materials
  • Browse materials
  • Articles
  • Conferences and seminars
  • Electronic books
  • Historical maps
  • Journals
  • Tunes and musical notes
  • Photographs
  • Presentations and posters
  • Publication series
  • Research reports
  • Research data
  • Study materials
  • Theses

Browse

All of JYXCollection listBy Issue DateAuthorsSubjectsPublished inDepartmentDiscipline

My Account

Login

Statistics

View Usage Statistics
  • How to publish in JYX?
  • Self-archiving
  • Publish Your Thesis Online
  • Publishing Your Dissertation
  • Publication services

Open Science at the JYU
 
Data Protection Description

Accessibility Statement

Unless otherwise specified, publicly available JYX metadata (excluding abstracts) may be freely reused under the CC0 waiver.
Open Science Centre