Nous démontrons l'existence de solutions singulières d'équations speciales lagrangiennes en dimension trois, dans le cas non convexe.
We prove the existence of non-smooth solutions to three-dimensional Special Lagrangian Equations in the non-convex case.
@article{AIHPC_2010__27_5_1179_0, author = {Nadirashvili, Nikolai and Vl\u{a}du\c{t}, Serge}, title = {Singular solution to {Special} {Lagrangian} {Equations}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1179--1188}, publisher = {Elsevier}, volume = {27}, number = {5}, year = {2010}, doi = {10.1016/j.anihpc.2010.05.001}, zbl = {1200.35123}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2010.05.001/} }
TY - JOUR AU - Nadirashvili, Nikolai AU - Vlăduţ, Serge TI - Singular solution to Special Lagrangian Equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 1179 EP - 1188 VL - 27 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2010.05.001/ DO - 10.1016/j.anihpc.2010.05.001 LA - en ID - AIHPC_2010__27_5_1179_0 ER -
%0 Journal Article %A Nadirashvili, Nikolai %A Vlăduţ, Serge %T Singular solution to Special Lagrangian Equations %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 1179-1188 %V 27 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2010.05.001/ %R 10.1016/j.anihpc.2010.05.001 %G en %F AIHPC_2010__27_5_1179_0
Nadirashvili, Nikolai; Vlăduţ, Serge. Singular solution to Special Lagrangian Equations. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 5, pp. 1179-1188. doi : 10.1016/j.anihpc.2010.05.001. http://www.numdam.org/articles/10.1016/j.anihpc.2010.05.001/
[1] Some theorems on partial differential equations of the second order, Vestnik Leningrad. Univ. 9 no. 8 (1954), 3-17
,[2] Convexity conditions and existence theorems in nonlinear elasticity, Arch. Ration. Mech. Anal. 63 (1977), 337-403 | Zbl
,[3] Liouville property and regularity of a Hessian quotient equation, Amer. J. Math. 125 no. 2 (2003), 301-316 | Zbl
, , , ,[4] Fully Nonlinear Elliptic Equations, Amer. Math. Soc., Providence, RI (1995) | Zbl
, ,[5] The Dirichlet problem for nonlinear second order elliptic equations III. Functions of the eigenvalues of the Hessian, Acta Math. 155 no. 3–4 (1985), 261-301 | Zbl
, , ,[6] A priori estimate for convex solutions to special Lagrangian equations and its application, Comm. Pure Appl. Math. 62 no. 4 (2009), 583-595 | Zbl
, , ,[7] Methods of Mathematical Physics. Vol. 2, Partial Differential Equations, Wiley (1989) | Zbl
, ,[8] User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.) 27 no. 1 (1992), 1-67 | Zbl
, , ,[9] An algebraic formula for the degree of a map germ, Ann. Math. 106 (1977), 19-44 | Zbl
, ,[10] Calibrated geometries, Acta Math. 148 (1982), 47-157 | Zbl
, ,[11] Dirichlet duality and the nonlinear Dirichlet problem, Comm. Pure Appl. Math. 62 no. 3 (2009), 396-443 | Zbl
, ,[12] On the general notion of fully nonlinear second-order elliptic equations, Trans. Amer. Math. Soc. 347 (1995), 857-895 | Zbl
,[13] Nonclassical solutions of fully nonlinear elliptic equations, Geom. Funct. Anal. 17 (2007), 1283-1296 | Zbl
, ,[14] Singular solutions to fully nonlinear elliptic equations, J. Math. Pures Appl. 89 (2008), 107-113 | Zbl
, ,[15] On Hessian fully nonlinear elliptic equations, arXiv:0805.2694 [math.AP] | Zbl
, ,[16] Hölder gradient estimates for fully nonlinear elliptic equations, Proc. Roy. Soc. Edinburgh Sect. A 108 no. 1–2 (1988), 57-65 | Zbl
,[17] On regularity and existence of viscosity solutions of nonlinear second order, elliptic equations, Progr. Nonlinear Differential Equations Appl. vol. 2, Birkhäuser Boston, Boston, MA (1989), 939-957
,[18] The Dirichlet problem for the prescribed curvature equations, Arch. Ration. Mech. Anal. 111 (1990), 153-170
,[19] A priori estimates for solutions of fully nonlinear special Lagrangian equations, Ann. Inst. H. Pioncaré Anal. Non Linéaire 18 (2001), 261-270 | EuDML | Numdam | Zbl
,Cité par Sources :