Classical, viscosity and average solutions for PDE’s with nonnegative characteristic form

Cristian E. Gutiérrez; Ermanno Lanconelli

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 1, page 17-28
  • ISSN: 1120-6330

Abstract

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We compare several definitions of weak solutions to second order partial differential equations with nonnegative characteristic form.

How to cite

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Gutiérrez, Cristian E., and Lanconelli, Ermanno. "Classical, viscosity and average solutions for PDE’s with nonnegative characteristic form." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 15.1 (2004): 17-28. <http://eudml.org/doc/252320>.

@article{Gutiérrez2004,
abstract = {We compare several definitions of weak solutions to second order partial differential equations with nonnegative characteristic form.},
author = {Gutiérrez, Cristian E., Lanconelli, Ermanno},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Weak solutions; Viscosity solutions; Second order PDE’s with nonnegative characteristic form; Second order PDE's with nonnegative characteristic form; asymptotic-average solution; -solution; Pizzeti formula},
language = {eng},
month = {3},
number = {1},
pages = {17-28},
publisher = {Accademia Nazionale dei Lincei},
title = {Classical, viscosity and average solutions for PDE’s with nonnegative characteristic form},
url = {http://eudml.org/doc/252320},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Gutiérrez, Cristian E.
AU - Lanconelli, Ermanno
TI - Classical, viscosity and average solutions for PDE’s with nonnegative characteristic form
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/3//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 1
SP - 17
EP - 28
AB - We compare several definitions of weak solutions to second order partial differential equations with nonnegative characteristic form.
LA - eng
KW - Weak solutions; Viscosity solutions; Second order PDE’s with nonnegative characteristic form; Second order PDE's with nonnegative characteristic form; asymptotic-average solution; -solution; Pizzeti formula
UR - http://eudml.org/doc/252320
ER -

References

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  13. PUCCI, C. - TALENTI, G., Elliptic (second-order) partial differential equations with measurable coefficients and approximating integral equations. Advances in Math., 19(1), 1976, 48-105. MR419989
  14. RAMASWAMY, S., Maximum principle for viscosity sub solutions and viscosity sub solutions of the Laplacian. Rend. Mat. Acc. Lincei, s. 9, v. 4, 1993, 213-217. Zbl0822.35019MR1250500
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