Let be an n-dimensional complete, non-compact and connected Riemannian manifold, with Ricci tensor and sectional curvature . Assume , and either and when for , or and . If , any solution of (E) on M satisfies for some constant . As a consequence, there exists such that any positive p-harmonic function v on M satisfies for any .
Soit une variété riemannienne n-dimensionnelle complète, non compacte et connexe de courbures de Ricci et sectionnelle . On suppose et si pour si , ou si . Si , toute solution de classe de (E) sur M satisfait à , où est une constante. On en déduit quʼil existe tel que toute fonction p-harmonique positive v sur M satisfait à lʼencadrement suivant : pour tout .
Accepted:
Published online:
@article{CRMATH_2013__351_11-12_445_0, author = {Bidaut-V\'eron, Marie-Fran\c{c}oise and Garcia-Huidobro, Marta and V\'eron, Laurent}, title = {Quasilinear elliptic {Hamilton{\textendash}Jacobi} equations on complete manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {445--449}, publisher = {Elsevier}, volume = {351}, number = {11-12}, year = {2013}, doi = {10.1016/j.crma.2013.06.007}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2013.06.007/} }
TY - JOUR AU - Bidaut-Véron, Marie-Françoise AU - Garcia-Huidobro, Marta AU - Véron, Laurent TI - Quasilinear elliptic Hamilton–Jacobi equations on complete manifolds JO - Comptes Rendus. Mathématique PY - 2013 SP - 445 EP - 449 VL - 351 IS - 11-12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2013.06.007/ DO - 10.1016/j.crma.2013.06.007 LA - en ID - CRMATH_2013__351_11-12_445_0 ER -
%0 Journal Article %A Bidaut-Véron, Marie-Françoise %A Garcia-Huidobro, Marta %A Véron, Laurent %T Quasilinear elliptic Hamilton–Jacobi equations on complete manifolds %J Comptes Rendus. Mathématique %D 2013 %P 445-449 %V 351 %N 11-12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2013.06.007/ %R 10.1016/j.crma.2013.06.007 %G en %F CRMATH_2013__351_11-12_445_0
Bidaut-Véron, Marie-Françoise; Garcia-Huidobro, Marta; Véron, Laurent. Quasilinear elliptic Hamilton–Jacobi equations on complete manifolds. Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 445-449. doi : 10.1016/j.crma.2013.06.007. http://archive.numdam.org/articles/10.1016/j.crma.2013.06.007/
[1] Differential equations on Riemannian manifolds and their geometric applications, Commun. Pure Appl. Math., Volume 28 (1975), pp. 333-354
[2] An excursion into geometric analysis (Grigorʼyan, A. et al., eds.), Surveys in Differential Geometry, vol. 9, International Press, Somerville, MA, 2004, pp. 83-146
[3] Function Theory on Manifolds which Possess a Pole, Lecture Notes in Mathematics, vol. 699, Springer-Verlag, Berlin, Heidelberg, 1979
[4] Local gradient estimates of p-harmonic functions, -flow, and an entropy formula, Ann. Sci. Éc. Norm. Supér., Volume 42 (2009), pp. 1-36
[5] Separable p-harmonic functions in a cone and related quasilinear equations on manifolds, J. Eur. Math. Soc., Volume 11 (2009), pp. 1285-1305
[6] Conformal immersion of complete Riemannian manifolds and extensions of the Schwarz lemma, Duke Math. J., Volume 74 (1994), pp. 223-236
Cited by Sources: