A robust linearisation scheme for a nonlinear elliptic boundary value problem: Error estimates

AbstractWe consider a nonlinear second-order elliptic boundary value problem in a bounded domain Ω ⊂ RN with mixed boundary conditions. The solution is found via linearisation. We design a robust and efficient approximation scheme. Error estimates for the linearisation algorithm are derived in L2(Ω), H1(Ω) and L∞(Ω) spaces under the minimal regularity assumptions of the exact solution.

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Compact embedding from W01,2(Ω) to Lq(x)(Ω) and its application to nonlinear elliptic boundary value problem with variable critical exponent

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2007.07.083 ◽

2008 ◽

Vol 339 (2) ◽

pp. 1386-1394 ◽

Cited By ~ 8

Author(s):

Kazuhiro Kurata ◽

Naoki Shioji

Keyword(s):

Boundary Value Problem ◽

Critical Exponent ◽

Elliptic Boundary ◽

Boundary Value ◽

Compact Embedding ◽

Elliptic Boundary Value Problem ◽

Elliptic Boundary Value ◽

Nonlinear Elliptic ◽

Nonlinear Elliptic Boundary

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A nonlinear elliptic boundary value problem at resonance

Journal of Differential Equations ◽

10.1016/0022-0396(77)90084-5 ◽

1977 ◽

Vol 26 (3) ◽

pp. 335-346 ◽

Cited By ~ 21

Author(s):

Howard Shaw

Keyword(s):

Boundary Value Problem ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problem ◽

Elliptic Boundary Value ◽

Nonlinear Elliptic ◽

At Resonance ◽

Nonlinear Elliptic Boundary ◽

Problem At Resonance

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On a Nonlinear Elliptic Boundary Value Problem

Proceedings of the American Mathematical Society ◽

10.2307/2040545 ◽

1975 ◽

Vol 50 (1) ◽

pp. 230

Author(s):

Nguyen Phuong Cac

Keyword(s):

Boundary Value Problem ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problem ◽

Elliptic Boundary Value ◽

Nonlinear Elliptic ◽

Nonlinear Elliptic Boundary

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Existence and uniqueness of solutions to a nonlinear elliptic boundary value problem on time scales

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2009.05.043 ◽

2010 ◽

Vol 15 (5) ◽

pp. 1124-1131 ◽

Cited By ~ 1

Author(s):

Aydin Huseynov

Keyword(s):

Boundary Value Problem ◽

Time Scales ◽

Existence And Uniqueness ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problem ◽

Uniqueness Of Solutions ◽

Elliptic Boundary Value ◽

Nonlinear Elliptic ◽

Nonlinear Elliptic Boundary

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On a singular nonlinear elliptic boundary-value problem

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1991-1037213-9 ◽

1991 ◽

Vol 111 (3) ◽

pp. 721-721 ◽

Cited By ~ 242

Author(s):

A. C. Lazer ◽

P. J. McKenna

Keyword(s):

Boundary Value Problem ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problem ◽

Elliptic Boundary Value ◽

Nonlinear Elliptic ◽

Nonlinear Elliptic Boundary

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Positive Solutions for a Class of Nonlinear Elliptic Boundary Value Problem

Advances in Applied Mathematics ◽

10.12677/aam.2018.77103 ◽

2018 ◽

Vol 07 (07) ◽

pp. 857-862

Author(s):

广军曲

Keyword(s):

Boundary Value Problem ◽

Positive Solutions ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problem ◽

Elliptic Boundary Value ◽

Nonlinear Elliptic ◽

Nonlinear Elliptic Boundary

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On a nonlinear elliptic boundary-value problem

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700024059 ◽

1975 ◽

Vol 12 (3) ◽

pp. 399-405 ◽

Cited By ~ 13

Author(s):

E.N. Dancer

Keyword(s):

Boundary Value Problem ◽

Boundary Value Problems ◽

Existence Of Solutions ◽

Elliptic Boundary ◽

Boundary Value ◽

Linear Part ◽

Elliptic Boundary Value Problem ◽

Elliptic Boundary Value ◽

Nonlinear Elliptic ◽

Nonlinear Elliptic Boundary

We announce a number of results on the existence of solutions of nonlinear elliptic boundary value problems in the case where the dominating linear part is not invertible. Our theorems improve recent results of Landesman and Lazer, and Williams.

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