Nonlinear Elliptic Equations with Lower Order Terms and Symmetrization Methods

Angelo Alvino; Anna Mercaldo

Bollettino dell'Unione Matematica Italiana (2008)

  • Volume: 1, Issue: 3, page 645-661
  • ISSN: 0392-4041

Abstract

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We consider the homogeneous Dirichlet problem for nonlinear elliptic equations as - div ⁡ a ⁢ ( x , ∇ ⁡ u ) = b ⁢ ( x , ∇ ⁡ u ) + μ where μ is a measure with bounded total variation. We fix structural conditions on functions a , b which ensure existence of solutions. Moreover, if μ is an L 1 function, we prove a uniqueness result under more restrictive hypotheses on the operator.

How to cite

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Alvino, Angelo, and Mercaldo, Anna. "Nonlinear Elliptic Equations with Lower Order Terms and Symmetrization Methods." Bollettino dell'Unione Matematica Italiana 1.3 (2008): 645-661. <http://eudml.org/doc/290453>.

@article{Alvino2008,
abstract = {We consider the homogeneous Dirichlet problem for nonlinear elliptic equations as \begin\{equation*\}-\operatorname\{div\} a(x, \nabla u) = b(x, \nabla u) + \mu \end\{equation*\} where $\mu$ is a measure with bounded total variation. We fix structural conditions on functions $a$, $b$ which ensure existence of solutions. Moreover, if $\mu$ is an $L^1$ function, we prove a uniqueness result under more restrictive hypotheses on the operator.},
author = {Alvino, Angelo, Mercaldo, Anna},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {645-661},
publisher = {Unione Matematica Italiana},
title = {Nonlinear Elliptic Equations with Lower Order Terms and Symmetrization Methods},
url = {http://eudml.org/doc/290453},
volume = {1},
year = {2008},
}

TY - JOUR
AU - Alvino, Angelo
AU - Mercaldo, Anna
TI - Nonlinear Elliptic Equations with Lower Order Terms and Symmetrization Methods
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/10//
PB - Unione Matematica Italiana
VL - 1
IS - 3
SP - 645
EP - 661
AB - We consider the homogeneous Dirichlet problem for nonlinear elliptic equations as \begin{equation*}-\operatorname{div} a(x, \nabla u) = b(x, \nabla u) + \mu \end{equation*} where $\mu$ is a measure with bounded total variation. We fix structural conditions on functions $a$, $b$ which ensure existence of solutions. Moreover, if $\mu$ is an $L^1$ function, we prove a uniqueness result under more restrictive hypotheses on the operator.
LA - eng
UR - http://eudml.org/doc/290453
ER -

References

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