An existence and approximation theorem for solutions of degenerate quasilinear elliptic equations

Albo Carlos Cavalheiro

Commentationes Mathematicae Universitatis Carolinae (2018)

  • Volume: 59, Issue: 1, page 65-80
  • ISSN: 0010-2628

Abstract

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The main result establishes that a weak solution of degenerate quasilinear elliptic equations can be approximated by a sequence of solutions for non-degenerate quasilinear elliptic equations.

How to cite

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Cavalheiro, Albo Carlos. "An existence and approximation theorem for solutions of degenerate quasilinear elliptic equations." Commentationes Mathematicae Universitatis Carolinae 59.1 (2018): 65-80. <http://eudml.org/doc/294833>.

@article{Cavalheiro2018,
abstract = {The main result establishes that a weak solution of degenerate quasilinear elliptic equations can be approximated by a sequence of solutions for non-degenerate quasilinear elliptic equations.},
author = {Cavalheiro, Albo Carlos},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {degenerate quasilinear elliptic equations; weighted Sobolev spaces},
language = {eng},
number = {1},
pages = {65-80},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {An existence and approximation theorem for solutions of degenerate quasilinear elliptic equations},
url = {http://eudml.org/doc/294833},
volume = {59},
year = {2018},
}

TY - JOUR
AU - Cavalheiro, Albo Carlos
TI - An existence and approximation theorem for solutions of degenerate quasilinear elliptic equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 1
SP - 65
EP - 80
AB - The main result establishes that a weak solution of degenerate quasilinear elliptic equations can be approximated by a sequence of solutions for non-degenerate quasilinear elliptic equations.
LA - eng
KW - degenerate quasilinear elliptic equations; weighted Sobolev spaces
UR - http://eudml.org/doc/294833
ER -

References

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  9. Kufner A., Weighted Sobolev Spaces, John Wiley & Sons, New York, 1985. Zbl0862.46017
  10. Muckenhoupt B., 10.1090/S0002-9947-1972-0293384-6, Trans. Amer. Math. Soc. 165 (1972), 207–226. DOI10.1090/S0002-9947-1972-0293384-6
  11. Torchinsky A., Real-Variable Methods in Harmonic Analysis, Academic Press, San Diego, 1986. Zbl1097.42002
  12. Turesson B. O., 10.1007/BFb0103912, Lecture Notes in Math., 1736, Springer, Berlin, 2000. DOI10.1007/BFb0103912
  13. Xu X., A local partial regularity theorem for weak solutions of degenerate elliptic equations and its applications to the thermistor problem, Differential Integral Equations 12 (1999), no. 1, 83–100. 
  14. Zeidler E., Nonlinear Functional Analysis and its Applications, II/B, Springer, New York, 1990. 

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