p x -harmonic functions with unbounded exponent in a subdomain

J. J. Manfredi; J. D. Rossi; J. M. Urbano

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 6, page 2581-2595
  • ISSN: 0294-1449

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Manfredi, J. J., Rossi, J. D., and Urbano, J. M.. "$p\left(x\right)$-harmonic functions with unbounded exponent in a subdomain." Annales de l'I.H.P. Analyse non linéaire 26.6 (2009): 2581-2595. <http://eudml.org/doc/78948>.

@article{Manfredi2009,
author = {Manfredi, J. J., Rossi, J. D., Urbano, J. M.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {-Laplacian; infinity-Laplacian; viscosity solutions},
language = {eng},
number = {6},
pages = {2581-2595},
publisher = {Elsevier},
title = {$p\left(x\right)$-harmonic functions with unbounded exponent in a subdomain},
url = {http://eudml.org/doc/78948},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Manfredi, J. J.
AU - Rossi, J. D.
AU - Urbano, J. M.
TI - $p\left(x\right)$-harmonic functions with unbounded exponent in a subdomain
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 6
SP - 2581
EP - 2595
LA - eng
KW - -Laplacian; infinity-Laplacian; viscosity solutions
UR - http://eudml.org/doc/78948
ER -

References

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  1. [1] Acerbi E., Mingione G., Regularity results for stationary electro-rheological fluids, Arch. Ration. Mech. Anal.164 (2002) 213-259. Zbl1038.76058MR1930392
  2. [2] Acerbi E., Mingione G., Gradient estimates for the p x -Laplacean system, J. Reine Angew. Math.584 (2005) 117-148. Zbl1093.76003MR2155087
  3. [3] Ambrosio L., Lecture notes on optimal transport problems, in: Mathematical Aspects of Evolving Interfaces, Funchal, 2000, Lecture Notes in Math., vol. 1812, Springer, Berlin, 2003, pp. 1-52. Zbl1047.35001MR2011032
  4. [4] Aronsson G., Extensions of functions satisfying Lipschitz conditions, Ark. Mat.6 (1967) 551-561. Zbl0158.05001MR217665
  5. [5] Aronsson G., Crandall M.G., Juutinen P., A tour of the theory of absolutely minimizing functions, Bull. Amer. Math. Soc.41 (2004) 439-505. Zbl1150.35047MR2083637
  6. [6] Barles G., Fully nonlinear Neumann type conditions for second-order elliptic and parabolic equations, J. Differential Equations106 (1993) 90-106. Zbl0786.35051MR1249178
  7. [7] Bhattacharya T., DiBenedetto E., Manfredi J., Limits as p of Δ p u p = f and related extremal problems, Rend. Semin. Mat. Univ. Politec. Torino1989 (1991) 15-68. MR1155453
  8. [8] Charro F., García Azorero J., Rossi J.D., A mixed problem for the infinity Laplacian via tug-of-war games, Calc. Var. Partial Differential Equations34 (2009) 307-320. Zbl1173.35459MR2471139
  9. [9] Crandall M.G., Ishii H., Lions P.L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc.27 (1992) 1-67. Zbl0755.35015MR1118699
  10. [10] Diening L., Hästö P., Nekvinda A., Open problems in variable exponent Lebesgue and Sobolev spaces, in: Drabek, Rakosnik (Eds.), FSDONA04 Proceedings, Milovy, Czech Republic, 2005, pp. 38-58. 
  11. [11] Harjulehto P., Hästö P., A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces, Rev. Mat. Complut.17 (2004) 129-146. Zbl1072.46021MR2063945
  12. [12] Harjulehto P., Hästö P., Koskenoja M., Varonen S., The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values, Potential Anal.25 (2006) 205-222. Zbl1120.46016MR2255345
  13. [13] Jensen R., Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient, Arch. Ration. Mech. Anal.123 (1993) 51-74. Zbl0789.35008MR1218686
  14. [14] Kováčik O., Rákosník J., On spaces L p x and W 1 , p x , Czechoslovak Math. J.41 (116) (1991) 592-618. Zbl0784.46029MR1134951
  15. [15] Lindqvist P., Notes on the p-Laplace equation, Report, University of Jyväskylä, Department of Mathematics and Statistics, 102, University of Jyväskylä, Jyväskylä, 2006; available on line at:, http://www.math.jyu.fi/research/reports/rep102.pdf. Zbl1256.35017MR2242021
  16. [16] Peres Y., Schramm O., Sheffield S., Wilson D.B., Tug-of-war and the infinity Laplacian, J. Amer. Math. Soc.22 (2009) 167-210. Zbl1206.91002MR2449057
  17. [17] Peres Y., Sheffield S., Tug-of-war with noise: A game theoretic view of the p-Laplacian, Duke Math. J.145 (2008) 91-120. Zbl1206.35112MR2451291

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