Jump to ContentJump to Main Navigation
Show Summary Details

Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Editorial Board Member: Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Strambach, Karl


IMPACT FACTOR 2015: 0.823
Rank 88 out of 312 in category Mathematics and 124 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 0.848
Source Normalized Impact per Paper (SNIP) 2015: 1.000
Impact per Publication (IPP) 2015: 0.606

Mathematical Citation Quotient (MCQ) 2015: 0.66

149,00 € / $224.00 / £112.00*

Online
ISSN
1435-5337
See all formats and pricing

 


Select Volume and Issue

Issues

Fractional estimates for non-differentiable elliptic systems with general growth

Citation Information: Forum Mathematicum. Volume 20, Issue 3, Pages 523–556, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/FORUM.2008.027, May 2008

Publication History

Received:
2006-10-06
Revised:
2006-11-29
Published Online:
2008-05-23

Abstract

In this paper we study the regularity of weak solutions of the elliptic system -div(A(x,∇u)) = b(x,∇u) with non-standard ϕ-growth condition. Here ϕ is a given Orlicz function. We are interested in the case where A and b are not differentiable with respect to x but only Hölder continuous with exponent α. We show that the natural quantity V(∇u) is locally in the Nikolskiĭ space N α, 2. From this it follows that the set of singularities of V(∇u) has Hausdorff dimension less or equal n – 2α, where n is the dimension of the domain Ω. One of the main features of our technique is that it handles the case of the p-Laplacian for 1 < p < ∞ in a unified way. There is no need to use different approaches for the cases p ≤ 2 and p ≥ 2.

2000 Mathematics Subject Classification: 35J60; 35D10.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Martin Kalousek
Nonlinear Analysis: Theory, Methods & Applications, 2016, Volume 136, Page 1
[2]
Dominic Breit and Martina Hofmanová
Comptes Rendus Mathematique, 2015
[4]
Dominic Breit, Lars Diening, and Sebastian Schwarzacher
SIAM Journal on Numerical Analysis, 2015, Volume 53, Number 1, Page 551
[5]
Václav Mácha and Jakub Tichý
Journal of Mathematical Fluid Mechanics, 2014, Volume 16, Number 4, Page 823
[6]
Dietmar Kröner, Michael Růžička, and Ioannis Toulopoulos
International Journal for Numerical Methods in Fluids, 2014, Volume 76, Number 11, Page 855
[7]
Paolo Baroni
Calculus of Variations and Partial Differential Equations, 2015, Volume 53, Number 3-4, Page 803
[8]
Sebastian Schwarzacher
Journal of Differential Equations, 2014, Volume 256, Number 7, Page 2423
[9]
L. Diening, P. Kaplicky, and S. Schwarzacher
Annali di Matematica Pura ed Applicata (1923 -), 2014, Volume 193, Number 6, Page 1779
[10]
Petr Kaplický and Jakub Tichý
Open Mathematics, 2013, Volume 11, Number 7
[11]
Flavia Giannetti and Antonia Passarelli di Napoli
Journal of Differential Equations, 2013, Volume 254, Number 3, Page 1280
[12]
L. Diening, D. Lengeler, B. Stroffolini, and A. Verde
SIAM Journal on Mathematical Analysis, 2012, Volume 44, Number 5, Page 3594
[13]
D. Breit
Nonlinear Analysis: Theory, Methods & Applications, 2012, Volume 75, Number 14, Page 5549
[14]
L. Diening and P. Kaplický
Manuscripta Mathematica, 2013, Volume 141, Number 1-2, Page 333
[15]
Lars Diening, Bianca Stroffolini, and Anna Verde
Journal of Differential Equations, 2012, Volume 253, Number 7, Page 1943
[16]
Adrian Hirn
Journal of Mathematical Fluid Mechanics, 2013, Volume 15, Number 1, Page 65
[17]
L. Belenki, L. C. Berselli, L. Diening, and M. Růžička
SIAM Journal on Numerical Analysis, 2012, Volume 50, Number 2, Page 373
[18]
L. Diening, P. Kaplický, and S. Schwarzacher
Nonlinear Analysis: Theory, Methods & Applications, 2012, Volume 75, Number 2, Page 637
[19]
Linda El Alaoui, Alexandre Ern, and Martin Vohralík
Computer Methods in Applied Mechanics and Engineering, 2011, Volume 200, Number 37-40, Page 2782
[20]
Dominic Breit, Bianca Stroffolini, and Anna Verde
Journal of Mathematical Analysis and Applications, 2011, Volume 383, Number 1, Page 226
[22]
Lars Diening, Bianca Stroffolini, and Anna Verde
ESAIM: Control, Optimisation and Calculus of Variations, 2011, Volume 17, Number 1, Page 178
[23]
Lars Diening and Christian Kreuzer
SIAM Journal on Numerical Analysis, 2008, Volume 46, Number 2, Page 614
[24]
Luigi C. Berselli, Lars Diening, and Michael Růžička
SIAM Journal on Numerical Analysis, 2009, Volume 47, Number 3, Page 2177

Comments (0)

Please log in or register to comment.