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 that includes the negative -Laplace operator, where 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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  1. Boccardo, L., Croce, G., 10.1515/9783110315424, De Gruyter Studies in Mathematics 55, De Gruyter, Berlin (2013). (2013) Zbl1293.35001MR3154599DOI10.1515/9783110315424
  2. Brezis, H., 10.1007/978-0-387-70914-7, Universitext, Springer, New York (2011). (2011) Zbl1220.46002MR2759829DOI10.1007/978-0-387-70914-7
  3. Chipot, M., 10.1007/978-3-7643-9982-5, Birkhäuser Advanced Texts. Basler Lehrbücher, Birkhäuser, Basel (2009). (2009) Zbl1171.35003MR2494977DOI10.1007/978-3-7643-9982-5
  4. Damascelli, L., 10.1016/S0294-1449(98)80032-2, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 15 (1998), 493-516. (1998) Zbl0911.35009MR1632933DOI10.1016/S0294-1449(98)80032-2
  5. D'Ambrosio, L., Farina, A., Mitidieri, E., Serrin, J., 10.1016/j.na.2013.06.004, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 90 (2013), 135-158. (2013) Zbl1287.35033MR3073634DOI10.1016/j.na.2013.06.004
  6. D'Ambrosio, L., Mitidieri, E., A priori estimates and reduction principles for quasilinear elliptic problems and applications, Adv. Differ. Equ. 17 (2012), 935-1000. (2012) Zbl1273.35138MR2985680
  7. Mitrović, D., Žubrinić, D., Fundamentals of Applied Functional Analysis. Distributions---Sobolev Spaces---Nonlinear Elliptic Equations, Pitman Monographs and Surveys in Pure and Applied Mathematics 91, Longman, Harlow (1998). (1998) Zbl0901.46001MR1603811
  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
  10. Unai, A., 10.17654/MS099060851, Far East J. Math. Sci. (FJMS) 99 (2016), 851-867. (2016) Zbl06627771MR3842964DOI10.17654/MS099060851

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