Neumann and second boundary value problems for hessian and Gauß curvature flows
Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 6, p. 1043-1073
@article{AIHPC_2003__20_6_1043_0,
     author = {Schn\"urer, Oliver C and Smoczyk, Knut},
     title = {Neumann and second boundary value problems for hessian and Gau\ss\ curvature flows},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {20},
     number = {6},
     year = {2003},
     pages = {1043-1073},
     doi = {10.1016/S0294-1449(03)00021-0},
     zbl = {1032.53058},
     mrnumber = {2008688},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2003__20_6_1043_0}
}
Schnürer, Oliver C; Smoczyk, Knut. Neumann and second boundary value problems for hessian and Gauß curvature flows. Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 6, pp. 1043-1073. doi : 10.1016/S0294-1449(03)00021-0. http://www.numdam.org/item/AIHPC_2003__20_6_1043_0/

[1] Andrews B, Gauß curvature flow, The shape of the rolling stones, Invent. Math. 138 (1999) 151-161. | MR 1714339 | Zbl 0936.35080

[2] Caffarelli L, Nirenberg L, Spruck J, Nonlinear second-order elliptic equations. V. The Dirichlet problem for Weingarten hypersurfaces, Comm. Pure Appl. Math. 41 (1988) 47-70. | MR 917124 | Zbl 0672.35028

[3] Chou K.-S, Wang X.-J, A logarithmic Gauß curvature flow and the Minkowski problem, Ann. Inst. H. Poincaré Analyse Non Linéaire 17 (6) (2000) 733-751. | Numdam | MR 1804653 | Zbl 1071.53534

[4] Chow B, Deforming convex hypersurfaces by the nth root of the Gaussian curvature, J. Differential Geom. 22 (1) (1985) 117-138. | MR 826427 | Zbl 0589.53005

[5] Daskalopoulos P, Hamilton R, The free boundary in the Gauß curvature flow with flat sides, J. Reine Angew. Math. 510 (1999) 187-227. | MR 1696096 | Zbl 0931.53031

[6] Firey W, Shapes of worn stones, Mathematica 21 (1974) 1-11. | MR 362045 | Zbl 0311.52003

[7] C. Gerhardt, Existenz für kleine Zeiten bei Neumann Randbedingungen, Lecture Notes.

[8] Gerhardt C, Hypersurfaces of prescribed curvature in Lorentzian manifolds, Indiana Univ. Math. J. 49 (2000) 1125-1153. | MR 1803223 | Zbl 1034.53064

[9] Gerhardt C, Hypersurfaces of prescribed Weingarten curvature, Math. Z. 224 (1997) 167-194. | MR 1431191 | Zbl 0871.53045

[10] Gilbarg D, Trudinger N.S, Elliptic Partial Differential Equations of Second Order, Grundlehren Math. Wiss., 224, Springer-Verlag, Berlin, 1983, xiii+513 pp. | MR 737190 | Zbl 0562.35001

[11] Ivochkina N.M, Ladyženskaja O.A, Estimation of the second derivatives on the boundary for surfaces evolving under the action of their principal curvatures, Algebra i Analiz 9 (1997) 30-50, (in Russian). Translation in , St. Petersburg Math. J. 9 (1998) 199-217. | MR 1468545 | Zbl 0893.35053

[12] Ladyženskaja O.A, Solonnikov V.A, Ural'Zeva N.N, Linear and Quasilinear Equations of Parabolic Type, (in Russian). Translated from the Russian by S. Smith , Transl. Math. Monographs, 23, American Mathematical Society, Providence, RI, 1967, xi+648 pp. | MR 241822 | Zbl 0174.15403

[13] Lieberman G.M, Second Order Parabolic Differential Equations, World Scientific, River Edge, NJ, 1996, xii+439 pp. | MR 1465184 | Zbl 0884.35001

[14] Lions P.-L, Trudinger N.S, Urbas J.I.E, The Neumann problem for equations of Monge-Ampère type, Comm. Pure Appl. Math. 39 (1986) 539-563. | MR 840340 | Zbl 0604.35027

[15] Schnürer O.C, The Dirichlet problem for Weingarten hypersurfaces in Lorentz manifolds, Math. Z. 242 (2002) 159-181. | MR 1985454 | Zbl 1042.53026

[16] Urbas J, Weingarten hypersurfaces with prescribed gradient image, Math. Z. 240 (2002) 53-82. | MR 1906707 | Zbl 01801578

[17] Urbas J, The second boundary value problem for a class of Hessian equations, Comm. Partial Differential Equations 26 (2001) 859-882. | MR 1843287 | Zbl 01658453

[18] Urbas J, Oblique boundary value problems for equations of Monge-Ampère type, Calc. Var. Partial Differential Equations 7 (1998) 19-39. | MR 1624426 | Zbl 0912.35068

[19] Urbas J, On the second boundary value problem for equations of Monge-Ampère type, J. Reine Angew. Math. 487 (1997) 115-124. | MR 1454261 | Zbl 0880.35031