Regularity of weak solutions to certain degenerate elliptic equations

Albo Carlos Cavalheiro

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 4, page 681-693
  • ISSN: 0010-2628

Abstract

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In this article we establish the existence of higher order weak derivatives of weak solutions of Dirichlet problem for a class of degenerate elliptic equations.

How to cite

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Cavalheiro, Albo Carlos. "Regularity of weak solutions to certain degenerate elliptic equations." Commentationes Mathematicae Universitatis Carolinae 47.4 (2006): 681-693. <http://eudml.org/doc/249852>.

@article{Cavalheiro2006,
abstract = {In this article we establish the existence of higher order weak derivatives of weak solutions of Dirichlet problem for a class of degenerate elliptic equations.},
author = {Cavalheiro, Albo Carlos},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {degenerate elliptic equations; weighted Sobolev spaces; degenerate elliptic equation; weighted Sobolev spaces},
language = {eng},
number = {4},
pages = {681-693},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Regularity of weak solutions to certain degenerate elliptic equations},
url = {http://eudml.org/doc/249852},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Cavalheiro, Albo Carlos
TI - Regularity of weak solutions to certain degenerate elliptic equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 4
SP - 681
EP - 693
AB - In this article we establish the existence of higher order weak derivatives of weak solutions of Dirichlet problem for a class of degenerate elliptic equations.
LA - eng
KW - degenerate elliptic equations; weighted Sobolev spaces; degenerate elliptic equation; weighted Sobolev spaces
UR - http://eudml.org/doc/249852
ER -

References

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  1. Fabes E., Jerison D., Kenig C., The Wiener test for degenerate elliptic equations, Ann. Inst. Fourier (Grenoble) 32 3 (1982), 151-182. (1982) MR0688024
  2. Fabes E., Kenig C., Serapioni R., The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations 7 1 (1982), 77-116. (1982) Zbl0498.35042MR0643158
  3. Franchi B., Serapioni R., Pointwise estimates for a class of strongly degenerate elliptic operators: a geometrical approach, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 4 (1987), 527-568. (1987) Zbl0685.35046MR0963489
  4. Garcia-Cuerva J., Rubio de Francia J., Weighted Norm Inequalities and Related Topics, North-Holland Mathematics Studies 116, North-Holland, Amsterdam, 1985. MR0848147
  5. Gilbarg D., Trudinger N., Elliptic Partial Differential Equations of Second Order, Springer, Berlin-New York, 1977. Zbl1042.35002MR0473443
  6. Heinonen J., Kilpeläinen T., Martio O., Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs, Oxford University Press, New York, 1993. MR1207810
  7. Muckenhoupt B., Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. (1972) Zbl0236.26016MR0293384
  8. Turesson B.O., Nonlinear potential theory and weighted Sobolev spaces, Lecture Notes in Math. 1736, Springer, Berlin, 2000. Zbl0949.31006MR1774162

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