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

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 Jan 1

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

Access to Document

10.1007/s00033-010-0080-5

Fingerprint Dive into the research topics of 'On Gaussian decay estimates of solutions to some linear elliptic equations and their applications'. Together they form a unique fingerprint.

Cite this

@article{98bd6f7316994b15bec42f094d250d08,

title = "On Gaussian decay estimates of solutions to some linear elliptic equations and their applications",

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",

author = "Yasunori Maekawa",

year = "2011",

month = jan,

day = "1",

doi = "10.1007/s00033-010-0080-5",

language = "English",

volume = "62",

pages = "1--30",

journal = "Zeitschrift fur Angewandte Mathematik und Physik",

issn = "0044-2275",

publisher = "Birkhauser Verlag Basel",

number = "1",

}

TY - JOUR

T1 - On Gaussian decay estimates of solutions to some linear elliptic equations and their applications

AU - Maekawa, Yasunori

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=79151476378&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79151476378&partnerID=8YFLogxK

U2 - 10.1007/s00033-010-0080-5

DO - 10.1007/s00033-010-0080-5

M3 - Article

AN - SCOPUS:79151476378

VL - 62

SP - 1

EP - 30

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 1

ER -