# Regularity of weak solutions to certain degenerate elliptic equations

Commentationes Mathematicae Universitatis Carolinae (2006)

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

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topCavalheiro, 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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- 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
- Garcia-Cuerva J., Rubio de Francia J., Weighted Norm Inequalities and Related Topics, North-Holland Mathematics Studies 116, North-Holland, Amsterdam, 1985. MR0848147
- Gilbarg D., Trudinger N., Elliptic Partial Differential Equations of Second Order, Springer, Berlin-New York, 1977. Zbl1042.35002MR0473443
- Heinonen J., Kilpeläinen T., Martio O., Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs, Oxford University Press, New York, 1993. MR1207810
- Muckenhoupt B., Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. (1972) Zbl0236.26016MR0293384
- Turesson B.O., Nonlinear potential theory and weighted Sobolev spaces, Lecture Notes in Math. 1736, Springer, Berlin, 2000. Zbl0949.31006MR1774162

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