Journal of the Mathematical Society of Japan

Resolutivity of ideal boundary for nonlinear Dirichlet problems

Fumi-Yuki MAEDA and Takayori ONO

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Abstract

We consider a quasi-linear second order elliptic differential equation on a euclidean domain. After developing necessary potential theory for the equation which extends some part of the theories in the book by Heinonen-Kilpeläinen-Martio, we show that the ideal boundary of the Royden type compactification of the domain is resolutive with respect to the Dirichlet problem for the equation.

Article information

Source
J. Math. Soc. Japan, Volume 52, Number 3 (2000), 561-581.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213107287

Digital Object Identifier
doi:10.2969/jmsj/05230561

Mathematical Reviews number (MathSciNet)
MR1760605

Zentralblatt MATH identifier
0958.31007

Subjects
Primary: 31C45: Other generalizations (nonlinear potential theory, etc.)
Secondary: 31B20: Boundary value and inverse problems

Keywords
Resolutivity of ideal boundary nonlinear Dirichlet problem

Citation

MAEDA, Fumi-Yuki; ONO, Takayori. Resolutivity of ideal boundary for nonlinear Dirichlet problems. J. Math. Soc. Japan 52 (2000), no. 3, 561--581. doi:10.2969/jmsj/05230561. https://projecteuclid.org/euclid.jmsj/1213107287


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