Maximum principle for viscosity sub solutions and viscosity sub solutions of the Laplacian

Sundararaja Ramaswamy

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993)

  • Volume: 4, Issue: 3, page 213-217
  • ISSN: 1120-6330

Abstract

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The aim of this paper is to characterize the u.s.c. (resp. l.s.c.) viscosity sub (resp. super) solutions of the Laplacian which do not take the value + ∞ (resp. - ∞ ) as precisely the sub (resp. super) harmonic functions.

How to cite

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Ramaswamy, Sundararaja. "Maximum principle for viscosity sub solutions and viscosity sub solutions of the Laplacian." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 4.3 (1993): 213-217. <http://eudml.org/doc/244138>.

@article{Ramaswamy1993,
abstract = {The aim of this paper is to characterize the u.s.c. (resp. l.s.c.) viscosity sub (resp. super) solutions of the Laplacian which do not take the value \( + \infty \) (resp. \( - \infty \)) as precisely the sub (resp. super) harmonic functions.},
author = {Ramaswamy, Sundararaja},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Viscosity solutions; Harmonic functions; Maximum principle; upper and lower semicontinuous sub- and super solutions},
language = {eng},
month = {9},
number = {3},
pages = {213-217},
publisher = {Accademia Nazionale dei Lincei},
title = {Maximum principle for viscosity sub solutions and viscosity sub solutions of the Laplacian},
url = {http://eudml.org/doc/244138},
volume = {4},
year = {1993},
}

TY - JOUR
AU - Ramaswamy, Sundararaja
TI - Maximum principle for viscosity sub solutions and viscosity sub solutions of the Laplacian
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1993/9//
PB - Accademia Nazionale dei Lincei
VL - 4
IS - 3
SP - 213
EP - 217
AB - The aim of this paper is to characterize the u.s.c. (resp. l.s.c.) viscosity sub (resp. super) solutions of the Laplacian which do not take the value \( + \infty \) (resp. \( - \infty \)) as precisely the sub (resp. super) harmonic functions.
LA - eng
KW - Viscosity solutions; Harmonic functions; Maximum principle; upper and lower semicontinuous sub- and super solutions
UR - http://eudml.org/doc/244138
ER -

References

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  1. CAFFARELLI, L. A., Interior a priori estimates for solutions of fully non-linear equations. Annals of Math., 130, 1989, 189-213. Zbl0692.35017MR1005611DOI10.2307/1971480
  2. ISHII, H. - LIONS, P. L., Viscosity solutions of fully non-linear second order elliptic partial differential equations. J. Diff. Eqns., 83, 1990, 26-78. Zbl0708.35031MR1031377DOI10.1016/0022-0396(90)90068-Z
  3. MYTHILY RAMASWAMY, - RAMASWAMY, S., Local property of viscosity solutions of fully non-linear second order elliptic partial differential Equations. Preprint. Zbl0867.35028

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