On the potential theory of some systems of coupled PDEs

Abderrahim Aslimani; Imad El Ghazi; Mohamed El Kadiri; Sabah Haddad

Commentationes Mathematicae Universitatis Carolinae (2016)

  • Volume: 57, Issue: 2, page 135-154
  • ISSN: 0010-2628

Abstract

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In this paper we study some potential theoretical properties of solutions and super-solutions of some PDE systems (S) of type L 1 u = - μ 1 v , L 2 v = - μ 2 u , on a domain D of ℝ d , where μ 1 and μ 2 are suitable measures on D , and L 1 , L 2 are two second order linear differential elliptic operators on D with coefficients of class 𝒞 ∞ . We also obtain the integral representation of the nonnegative solutions and supersolutions of the system (S) by means of the Green kernels and Martin boundaries associated with L 1 and L 2 , and a convergence property for increasing sequences of solutions of (S).

How to cite

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Aslimani, Abderrahim, et al. "On the potential theory of some systems of coupled PDEs." Commentationes Mathematicae Universitatis Carolinae 57.2 (2016): 135-154. <http://eudml.org/doc/280141>.

@article{Aslimani2016,
abstract = {In this paper we study some potential theoretical properties of solutions and super-solutions of some PDE systems (S) of type $L_1u =-\mu _1v$, $L_2v =-\mu _2u$, on a domain $D$ of $\mathbb \{R\}^d$, where $\mu _1$ and $\mu _2$ are suitable measures on $D$, and $L_1$, $L_2$ are two second order linear differential elliptic operators on $D$ with coefficients of class $\mathcal \{C\}^\infty $. We also obtain the integral representation of the nonnegative solutions and supersolutions of the system (S) by means of the Green kernels and Martin boundaries associated with $L_1$ and $L_2$, and a convergence property for increasing sequences of solutions of (S).},
author = {Aslimani, Abderrahim, El Ghazi, Imad, El Kadiri, Mohamed, Haddad, Sabah},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {harmonic function; superharmonic function; potential; elliptic linear differential operator; kernel; coupled PDEs system; Kato measure},
language = {eng},
number = {2},
pages = {135-154},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the potential theory of some systems of coupled PDEs},
url = {http://eudml.org/doc/280141},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Aslimani, Abderrahim
AU - El Ghazi, Imad
AU - El Kadiri, Mohamed
AU - Haddad, Sabah
TI - On the potential theory of some systems of coupled PDEs
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 2
SP - 135
EP - 154
AB - In this paper we study some potential theoretical properties of solutions and super-solutions of some PDE systems (S) of type $L_1u =-\mu _1v$, $L_2v =-\mu _2u$, on a domain $D$ of $\mathbb {R}^d$, where $\mu _1$ and $\mu _2$ are suitable measures on $D$, and $L_1$, $L_2$ are two second order linear differential elliptic operators on $D$ with coefficients of class $\mathcal {C}^\infty $. We also obtain the integral representation of the nonnegative solutions and supersolutions of the system (S) by means of the Green kernels and Martin boundaries associated with $L_1$ and $L_2$, and a convergence property for increasing sequences of solutions of (S).
LA - eng
KW - harmonic function; superharmonic function; potential; elliptic linear differential operator; kernel; coupled PDEs system; Kato measure
UR - http://eudml.org/doc/280141
ER -

References

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