On Gaussian decay estimates of solutions to some linear elliptic equations and their applications

Yasunori Maekawa

doi:10.1007/s00033-010-0080-5

On Gaussian decay estimates of solutions to some linear elliptic equations and their applications

Yasunori Maekawa

SCI - Mathematics

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

2 Citations (Scopus)

Abstract

In this paper we establish pointwise decay estimates of solutions to some linear elliptic equations by using the Nash-Moser iteration arguments and the ODE method. As applications we obtain sharp Gaussian decay estimates for solutions to nonlinear elliptic equations that are related with self-similar solutions to nonlinear heat equations and standing wave solutions to nonlinear Schrödinger equations with harmonic potential.

Original language	English
Pages (from-to)	1-30
Number of pages	30
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	62
Issue number	1
DOIs	https://doi.org/10.1007/s00033-010-0080-5
Publication status	Published - 2011 Feb

Keywords

Elliptic equations
Gaussian decay estimates
Nonlinear convection-diffusion equations
Standing wave solutions to nonlinear Schrödinger equations
The Haraux-Weissler equations

ASJC Scopus subject areas

Mathematics(all)
Physics and Astronomy(all)
Applied Mathematics

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10.1007/s00033-010-0080-5

Cite this

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abstract = "In this paper we establish pointwise decay estimates of solutions to some linear elliptic equations by using the Nash-Moser iteration arguments and the ODE method. As applications we obtain sharp Gaussian decay estimates for solutions to nonlinear elliptic equations that are related with self-similar solutions to nonlinear heat equations and standing wave solutions to nonlinear Schr{\"o}dinger equations with harmonic potential.",

keywords = "Elliptic equations, Gaussian decay estimates, Nonlinear convection-diffusion equations, Standing wave solutions to nonlinear Schr{\"o}dinger equations, The Haraux-Weissler equations",

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AB - In this paper we establish pointwise decay estimates of solutions to some linear elliptic equations by using the Nash-Moser iteration arguments and the ODE method. As applications we obtain sharp Gaussian decay estimates for solutions to nonlinear elliptic equations that are related with self-similar solutions to nonlinear heat equations and standing wave solutions to nonlinear Schrödinger equations with harmonic potential.

KW - Elliptic equations

KW - Gaussian decay estimates

KW - Nonlinear convection-diffusion equations

KW - Standing wave solutions to nonlinear Schrödinger equations

KW - The Haraux-Weissler equations

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IS - 1

ER -

On Gaussian decay estimates of solutions to some linear elliptic equations and their applications

Abstract

Keywords

ASJC Scopus subject areas

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