A weak comparison principle for some quasilinear elliptic operators: it compares functions belonging to different spaces

Akihito Unai

Applications of Mathematics (2018)

  • Volume: 63, Issue: 4, page 483-498
  • ISSN: 0862-7940

Abstract

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We shall prove a weak comparison principle for quasilinear elliptic operators - div ( a ( x , ∇ u ) ) that includes the negative p -Laplace operator, where a : Ω × ℝ N → ℝ N satisfies certain conditions frequently seen in the research of quasilinear elliptic operators. In our result, it is characteristic that functions which are compared belong to different spaces.

How to cite

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Unai, Akihito. "A weak comparison principle for some quasilinear elliptic operators: it compares functions belonging to different spaces." Applications of Mathematics 63.4 (2018): 483-498. <http://eudml.org/doc/294168>.

@article{Unai2018,
abstract = {We shall prove a weak comparison principle for quasilinear elliptic operators $-\{\rm div\}(a(x,\nabla u))$ that includes the negative $p$-Laplace operator, where $a\colon \Omega \times \mathbb \{R\}^N \rightarrow \mathbb \{R\}^N$ satisfies certain conditions frequently seen in the research of quasilinear elliptic operators. In our result, it is characteristic that functions which are compared belong to different spaces.},
author = {Unai, Akihito},
journal = {Applications of Mathematics},
keywords = {weak comparison principle; quasilinear elliptic operator; $p$-Laplace operator},
language = {eng},
number = {4},
pages = {483-498},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A weak comparison principle for some quasilinear elliptic operators: it compares functions belonging to different spaces},
url = {http://eudml.org/doc/294168},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Unai, Akihito
TI - A weak comparison principle for some quasilinear elliptic operators: it compares functions belonging to different spaces
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 4
SP - 483
EP - 498
AB - We shall prove a weak comparison principle for quasilinear elliptic operators $-{\rm div}(a(x,\nabla u))$ that includes the negative $p$-Laplace operator, where $a\colon \Omega \times \mathbb {R}^N \rightarrow \mathbb {R}^N$ satisfies certain conditions frequently seen in the research of quasilinear elliptic operators. In our result, it is characteristic that functions which are compared belong to different spaces.
LA - eng
KW - weak comparison principle; quasilinear elliptic operator; $p$-Laplace operator
UR - http://eudml.org/doc/294168
ER -

References

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  8. Motreanu, D., Motreanu, V. V., Papageorgiou, N., 10.1007/978-1-4614-9323-5, Springer, New York (2014). (2014) Zbl1292.47001MR3136201DOI10.1007/978-1-4614-9323-5
  9. Tolksdorf, P., 10.1080/03605308308820285, Commun. Partial Differ. Equations 8 (1983), 773-817. (1983) Zbl0515.35024MR0700735DOI10.1080/03605308308820285
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