Embeddings of weighted Sobolev spaces and a weighted fourth-order elliptic equation

Zongming Guo; Fangshu Wan; Liping Wang

doi:10.1142/S0219199719500573

Embeddings of weighted Sobolev spaces and a weighted fourth-order elliptic equation

Zongming Guo
, Fangshu Wan
, Liping Wang^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

New embeddings of weighted Sobolev spaces are established. Using such embeddings, we obtain the existence and regularity of positive solutions with Navier boundary value problems for a weighted fourth-order elliptic equation. We also obtain Liouville type results for the related equation. Some problems are still open.

Original language	English
Article number	1950057
Journal	Communications in Contemporary Mathematics
Volume	22
Issue number	6
DOIs	https://doi.org/10.1142/S0219199719500573
State	Published - 1 Sep 2020

Keywords

Liouville theorem
Positive solutions
fourth-order with weights

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10.1142/S0219199719500573

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title = "Embeddings of weighted Sobolev spaces and a weighted fourth-order elliptic equation",

abstract = "New embeddings of weighted Sobolev spaces are established. Using such embeddings, we obtain the existence and regularity of positive solutions with Navier boundary value problems for a weighted fourth-order elliptic equation. We also obtain Liouville type results for the related equation. Some problems are still open.",

keywords = "Liouville theorem, Positive solutions, fourth-order with weights",

author = "Zongming Guo and Fangshu Wan and Liping Wang",

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year = "2020",

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T1 - Embeddings of weighted Sobolev spaces and a weighted fourth-order elliptic equation

AU - Guo, Zongming

AU - Wan, Fangshu

AU - Wang, Liping

PY - 2020/9/1

Y1 - 2020/9/1

N2 - New embeddings of weighted Sobolev spaces are established. Using such embeddings, we obtain the existence and regularity of positive solutions with Navier boundary value problems for a weighted fourth-order elliptic equation. We also obtain Liouville type results for the related equation. Some problems are still open.

AB - New embeddings of weighted Sobolev spaces are established. Using such embeddings, we obtain the existence and regularity of positive solutions with Navier boundary value problems for a weighted fourth-order elliptic equation. We also obtain Liouville type results for the related equation. Some problems are still open.

KW - Liouville theorem

KW - Positive solutions

KW - fourth-order with weights

UR - https://www.scopus.com/pages/publications/85071010353

U2 - 10.1142/S0219199719500573

DO - 10.1142/S0219199719500573

M3 - 文章

AN - SCOPUS:85071010353

SN - 0219-1997

VL - 22

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - 6

M1 - 1950057

ER -

Embeddings of weighted Sobolev spaces and a weighted fourth-order elliptic equation

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Keywords

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