The existence of solutions to certain quasilinear elliptic equations

Tsang Hai Kuo; Yi Jung Chen

doi:10.1016/j.na.2010.10.001

The existence of solutions to certain quasilinear elliptic equations

Tsang Hai Kuo^*
, Yi Jung Chen

^*Corresponding author for this work

Center for General Education

Tamkang University

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

Abstract

Let Lu=-∑_i,j=1^Na_ij(x,u)Diju+c(x,u)u. Consider the quasilinear elliptic equation Lu=f(x,u,∇u) on a bounded smooth domain Ω in ℝ^N, where c(x,r)<α>0, f(x,r,ξ)=o[|r|+h(|r|)|ξ|²]. It is shown that if the oscillation of aij(x,r) with respect to r is sufficiently small, then there exists a solution u∈W^2,p(Ω)∩W₀ ^1,p(Ω) to the equation Lu=f(x,u,∇u).

Original language	English
Pages (from-to)	1286-1289
Number of pages	4
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	74
Issue number	4
DOIs	https://doi.org/10.1016/j.na.2010.10.001
State	Published - 15 02 2011

Keywords

Quasilinear elliptic equation
W (Ω)∩W (Ω) solution
W-estimate

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10.1016/j.na.2010.10.001

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title = "The existence of solutions to certain quasilinear elliptic equations",

abstract = "Let Lu=-∑i,j=1Naij(x,u)Diju+c(x,u)u. Consider the quasilinear elliptic equation Lu=f(x,u,∇u) on a bounded smooth domain Ω in ℝN, where c(x,r)<α>0, f(x,r,ξ)=o[|r|+h(|r|)|ξ|2]. It is shown that if the oscillation of aij(x,r) with respect to r is sufficiently small, then there exists a solution u∈W2,p(Ω)∩W0 1,p(Ω) to the equation Lu=f(x,u,∇u).",

keywords = "Quasilinear elliptic equation, W (Ω)∩W (Ω) solution, W-estimate",

author = "Kuo, \{Tsang Hai\} and Chen, \{Yi Jung\}",

year = "2011",

month = feb,

day = "15",

doi = "10.1016/j.na.2010.10.001",

language = "英语",

volume = "74",

pages = "1286--1289",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

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}

TY - JOUR

T1 - The existence of solutions to certain quasilinear elliptic equations

AU - Kuo, Tsang Hai

AU - Chen, Yi Jung

PY - 2011/2/15

Y1 - 2011/2/15

N2 - Let Lu=-∑i,j=1Naij(x,u)Diju+c(x,u)u. Consider the quasilinear elliptic equation Lu=f(x,u,∇u) on a bounded smooth domain Ω in ℝN, where c(x,r)<α>0, f(x,r,ξ)=o[|r|+h(|r|)|ξ|2]. It is shown that if the oscillation of aij(x,r) with respect to r is sufficiently small, then there exists a solution u∈W2,p(Ω)∩W0 1,p(Ω) to the equation Lu=f(x,u,∇u).

AB - Let Lu=-∑i,j=1Naij(x,u)Diju+c(x,u)u. Consider the quasilinear elliptic equation Lu=f(x,u,∇u) on a bounded smooth domain Ω in ℝN, where c(x,r)<α>0, f(x,r,ξ)=o[|r|+h(|r|)|ξ|2]. It is shown that if the oscillation of aij(x,r) with respect to r is sufficiently small, then there exists a solution u∈W2,p(Ω)∩W0 1,p(Ω) to the equation Lu=f(x,u,∇u).

KW - Quasilinear elliptic equation

KW - W (Ω)∩W (Ω) solution

KW - W-estimate

UR - https://www.scopus.com/pages/publications/78650514690

U2 - 10.1016/j.na.2010.10.001

DO - 10.1016/j.na.2010.10.001

M3 - 文章

AN - SCOPUS:78650514690

SN - 0362-546X

VL - 74

SP - 1286

EP - 1289

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 4

ER -

The existence of solutions to certain quasilinear elliptic equations

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Keywords

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