The Neumann problem for some degenerate elliptic equations

Albo Carlos Cavalheiro

Applications of Mathematics (2006)

  • Volume: 51, Issue: 6, page 619-628
  • ISSN: 0862-7940

Abstract

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In the paper we study the equation L u = f , where L is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set Ω . We prove existence and uniqueness of solutions in the space H ( Ω ) for the Neumann problem.

How to cite

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Cavalheiro, Albo Carlos. "The Neumann problem for some degenerate elliptic equations." Applications of Mathematics 51.6 (2006): 619-628. <http://eudml.org/doc/33271>.

@article{Cavalheiro2006,
abstract = {In the paper we study the equation $Lu=f$, where $L$ is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set $\{\Omega \}$. We prove existence and uniqueness of solutions in the space $H(\Omega )$ for the Neumann problem.},
author = {Cavalheiro, Albo Carlos},
journal = {Applications of Mathematics},
keywords = {Neumann problem; degenerate elliptic equations; Neumann problem; degenerate elliptic equations},
language = {eng},
number = {6},
pages = {619-628},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Neumann problem for some degenerate elliptic equations},
url = {http://eudml.org/doc/33271},
volume = {51},
year = {2006},
}

TY - JOUR
AU - Cavalheiro, Albo Carlos
TI - The Neumann problem for some degenerate elliptic equations
JO - Applications of Mathematics
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 6
SP - 619
EP - 628
AB - In the paper we study the equation $Lu=f$, where $L$ is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set ${\Omega }$. We prove existence and uniqueness of solutions in the space $H(\Omega )$ for the Neumann problem.
LA - eng
KW - Neumann problem; degenerate elliptic equations; Neumann problem; degenerate elliptic equations
UR - http://eudml.org/doc/33271
ER -

References

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  8. Nonlinear Potential Theory of Degenerate Elliptic Equations. Oxford Math. Monographs, Clarendon Press, Oxford, 1993. (1993) MR1207810
  9. Weighted Norm Inequalities and Related Topics. North-Holland Mathematics Studies  116, North Holland, Amsterdam-New York-Oxford, 1985. (1985) MR0807149
  10. Nonlinear Potential Theory and Weighted Sobolev Spaces. Lectures Notes in Mathematics Vol.  1736, Springer-Verlag, Berlin, 2000. (2000) MR1774162
  11. 10.1016/0362-546X(94)90165-1, Nonlinear Anal., Theory Methods Appl. 22 (1994), 409–424. (1994) MR1266369DOI10.1016/0362-546X(94)90165-1

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