[Solutions visqueuses du problème avec une dérivée oblique dégénérée pour une classe d'équations complètement non linéaires]
On démontre dans cette Note un principe de comparaison entre les sous et supersolutions visqueuses semi-continues du problème avec une dérivée oblique tangentielle et aussi le problème mixte du type de Dirichlet–Neumann pour une classe d'équations elliptiques complètement non-linéaires. En appliquant ce principe de comparaison on démontre l'existence d'une solution visqueuse unique.
In this paper we prove a comparison principle between the semicontinuous viscosity sub- and supersolutions of the tangential oblique derivative problem and the mixed Dirichlet–Neumann problem for fully nonlinear elliptic equations. By means of the comparison principle, the existence of a unique viscosity solution is obtained.
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@article{CRMATH_2002__334_8_661_0,
author = {Popivanov, Petar and Kutev, Nickolai},
title = {Viscosity solutions to the degenerate oblique derivative problem for fully nonlinear elliptic equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {661--666},
publisher = {Elsevier},
volume = {334},
number = {8},
year = {2002},
doi = {10.1016/S1631-073X(02)02321-X},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02321-X/}
}
TY - JOUR AU - Popivanov, Petar AU - Kutev, Nickolai TI - Viscosity solutions to the degenerate oblique derivative problem for fully nonlinear elliptic equations JO - Comptes Rendus. Mathématique PY - 2002 SP - 661 EP - 666 VL - 334 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02321-X/ DO - 10.1016/S1631-073X(02)02321-X LA - en ID - CRMATH_2002__334_8_661_0 ER -
%0 Journal Article %A Popivanov, Petar %A Kutev, Nickolai %T Viscosity solutions to the degenerate oblique derivative problem for fully nonlinear elliptic equations %J Comptes Rendus. Mathématique %D 2002 %P 661-666 %V 334 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02321-X/ %R 10.1016/S1631-073X(02)02321-X %G en %F CRMATH_2002__334_8_661_0
Popivanov, Petar; Kutev, Nickolai. Viscosity solutions to the degenerate oblique derivative problem for fully nonlinear elliptic equations. Comptes Rendus. Mathématique, Tome 334 (2002) no. 8, pp. 661-666. doi : 10.1016/S1631-073X(02)02321-X. http://www.numdam.org/articles/10.1016/S1631-073X(02)02321-X/
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