On parabolic initial-boundary value problems with critical growth for the gradient

Rüdiger Landes; Vesa Mustonen

Annales de l'I.H.P. Analyse non linéaire (1994)

  • Volume: 11, Issue: 2, page 135-158
  • ISSN: 0294-1449

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Landes, Rüdiger, and Mustonen, Vesa. "On parabolic initial-boundary value problems with critical growth for the gradient." Annales de l'I.H.P. Analyse non linéaire 11.2 (1994): 135-158. <http://eudml.org/doc/78326>.

@article{Landes1994,
author = {Landes, Rüdiger, Mustonen, Vesa},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {lack of compactness; Leray-Lions type operator; critical growth},
language = {eng},
number = {2},
pages = {135-158},
publisher = {Gauthier-Villars},
title = {On parabolic initial-boundary value problems with critical growth for the gradient},
url = {http://eudml.org/doc/78326},
volume = {11},
year = {1994},
}

TY - JOUR
AU - Landes, Rüdiger
AU - Mustonen, Vesa
TI - On parabolic initial-boundary value problems with critical growth for the gradient
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1994
PB - Gauthier-Villars
VL - 11
IS - 2
SP - 135
EP - 158
LA - eng
KW - lack of compactness; Leray-Lions type operator; critical growth
UR - http://eudml.org/doc/78326
ER -

References

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  1. [BBM] A. Bensoussan, L. Boccardo and F. Murat, On a Nonlinear P.D.E. having Natural Growth Terms and Unbounded Solutions, Annales de l'Inst. H. Poincaré, Analyse non linéaire, Vol. 5, 1988, pp. 347-364. Zbl0696.35042MR963104
  2. [BM] L. Boccardo and F. Murat, Almost Everywhere Convergence of the Gradients of Solutions to Elliptic and Parabolic Equations Divergence Form, Nonlinear Analysis, T.M.A., Vol. 19, 1992, pp. 581-592. Zbl0783.35020MR1183665
  3. [B] F. Browder, Strongly Nonlinear Parabolic Equations of Higher Order, Atti Acc. Lincei, Vol. 77, 1986, pp. 159-172. 
  4. [D] T. Del-Vecchio, Strongly Nonlinear Problems with Hamiltonian having Natural Growth, Houston J. of Math., Vol. 16, 1990. Zbl0714.35035MR1071263
  5. [F] J. Frehse, Existence and Perturbation Theorems for Nonlinear Elliptic Systems, Preprint, No. 576, Bonn, 1983. Zbl0528.35036MR716513
  6. [La1] R. Landes, On Galerkin's Method in the Existence Theory of Quasilinear Elliptic Equations, J. Functional Analysis, Vol. 39, 1980, pp. 123-148. Zbl0452.35037MR597807
  7. [La2] R. Landes, On the Existence of Weak Solutions for Quasilinear Parabolic Initial-Boundary Value Problems, Proc. Roy. Soc. Edinburgh Sect. A., Vol. 89, 1981, pp. 217-237. Zbl0493.35054MR635759
  8. [La3] R. Landes, Solvability of Perturbed Elliptic Equations with Critical Growth Exponent for the Gradient, J. Math.Analysis Appl., Vol. 139, 1989, pp. 63-77. Zbl0691.35038MR991927
  9. [La4] R. Landes, On the Existence of weak Solutions of Perturbed Systems with Critical Growth, J. Reine Angew. Math., Vol. 393, 1989, pp. 21-38. Zbl0664.35027MR972359
  10. [LM] R. Landes and V. Mustonen, A Strong Nonlinear Parabolic Initial Boundary Value Problem, Arkiv for Matematik, Vol. 25, 1987, pp. 29-40. Zbl0697.35071MR918378
  11. [Li] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Gauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
  12. [Z] E. Zeidler, Nonlinear Functional Analysis and its Applications, IIA and IIB, Springer-Verlag, New York-Berlin-Heidelberg, 1990. 

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