[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.
Accepté le :
Publié le :
Petar Popivanov 1 ; Nickolai Kutev 1
@article{CRMATH_2002__334_8_661_0,
author = {Petar Popivanov and Nickolai Kutev},
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},
}
TY - JOUR AU - Petar Popivanov AU - Nickolai Kutev 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 DO - 10.1016/S1631-073X(02)02321-X LA - en ID - CRMATH_2002__334_8_661_0 ER -
%0 Journal Article %A Petar Popivanov %A Nickolai Kutev %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 %R 10.1016/S1631-073X(02)02321-X %G en %F CRMATH_2002__334_8_661_0
Petar Popivanov; Nickolai Kutev. Viscosity solutions to the degenerate oblique derivative problem for fully nonlinear elliptic equations. Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 661-666. doi : 10.1016/S1631-073X(02)02321-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02321-X/
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