Neumann and second boundary value problems for hessian and Gauß curvature flows
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 6, pp. 1043-1073.
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     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},
     pages = {1043--1073},
     publisher = {Elsevier},
     volume = {20},
     number = {6},
     year = {2003},
     doi = {10.1016/S0294-1449(03)00021-0},
     mrnumber = {2008688},
     zbl = {1032.53058},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/S0294-1449(03)00021-0/}
}
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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, Tome 20 (2003) no. 6, pp. 1043-1073. doi : 10.1016/S0294-1449(03)00021-0. https://www.numdam.org/articles/10.1016/S0294-1449(03)00021-0/

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

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

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

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

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

  • Wang, Chong; Huang, Rongli; Bao, Jiguang On the second boundary value problem for a class of fully nonlinear flow III, Journal of Evolution Equations, Volume 24 (2024) no. 3 | DOI:10.1007/s00028-024-00983-6
  • An, Ning; Bao, Jiguang; Liu, Zixiao Entire solutions to the parabolic Monge–Ampère equation with unbounded nonlinear growth in time, Nonlinear Analysis, Volume 239 (2024), p. 113441 | DOI:10.1016/j.na.2023.113441
  • Wang, Chong; Huang, Rongli; Bao, Jiguang On the second boundary value problem for Lagrangian mean curvature equation, Calculus of Variations and Partial Differential Equations, Volume 62 (2023) no. 3 | DOI:10.1007/s00526-022-02412-3
  • Huang, Rongli; Li, Sitong On the second boundary value problem for special Lagrangian curvature potential equation, Mathematische Zeitschrift, Volume 302 (2022) no. 1, p. 391 | DOI:10.1007/s00209-022-03060-1
  • Chen, Chuan Qiang; Ma, Xi Nan; Zhang, De Kai The Neumann Problem for Parabolic Hessian Quotient Equations, Acta Mathematica Sinica, English Series, Volume 37 (2021) no. 9, p. 1313 | DOI:10.1007/s10114-021-0340-7
  • Xiao, Ling Neumann boundary value problem for general curvature flow with forcing term, Geometriae Dedicata, Volume 213 (2021) no. 1, p. 345 | DOI:10.1007/s10711-020-00585-9
  • Maeta, Shun Self-similar solutions to the Hesse flow, Information Geometry, Volume 4 (2021) no. 2, p. 313 | DOI:10.1007/s41884-021-00054-6
  • Berman, Robert J. The Sinkhorn algorithm, parabolic optimal transport and geometric Monge–Ampère equations, Numerische Mathematik, Volume 145 (2020) no. 4, p. 771 | DOI:10.1007/s00211-020-01127-x
  • Huang, Rongli; Ye, Yunhua On the Second Boundary Value Problem for a Class of Fully Nonlinear Flows I, International Mathematics Research Notices, Volume 2019 (2019) no. 18, p. 5539 | DOI:10.1093/imrn/rnx278
  • Chen, Juanjuan; Huang, Rongli; Ye, Yunhua On the second boundary value problem for a class of fully nonlinear flows II, Archiv der Mathematik, Volume 111 (2018) no. 4, p. 407 | DOI:10.1007/s00013-018-1197-6
  • Huang, Rongli; Ou, Qianzhong On the Second Boundary Value Problem for a Class of Fully Nonlinear Equations, The Journal of Geometric Analysis, Volume 27 (2017) no. 4, p. 2601 | DOI:10.1007/s12220-017-9774-7
  • Huang, Rongli On the second boundary value problem for Lagrangian mean curvature flow, Journal of Functional Analysis, Volume 269 (2015) no. 4, p. 1095 | DOI:10.1016/j.jfa.2015.05.003
  • Dai, Limei Exterior problems for more general parabolic Monge–Ampère equation in more general domain, Journal of Mathematical Analysis and Applications, Volume 427 (2015) no. 2, p. 1190 | DOI:10.1016/j.jmaa.2015.02.087
  • Wang, Juan; Yang, Jinlin; Liu, Xinzhi The Initial and Neumann Boundary Value Problem for a Class Parabolic Monge-Ampère Equation, Abstract and Applied Analysis, Volume 2013 (2013), p. 1 | DOI:10.1155/2013/535629
  • Wang, Juan; Liu, Huizhao; Yang, Jinlin The Initial and Neumann Boundary Value Problem for A Class Parabolic Monge–Ampère Equation, Green Communications and Networks, Volume 113 (2012), p. 699 | DOI:10.1007/978-94-007-2169-2_82
  • Huijuan Jia; Zhenghui Guo; Yanfei Liu, 2011 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce (AIMSEC) (2011), p. 2292 | DOI:10.1109/aimsec.2011.6010936
  • Sulman, Mohamed M.; Williams, J.F.; Russell, Robert D. An efficient approach for the numerical solution of the Monge–Ampère equation, Applied Numerical Mathematics, Volume 61 (2011) no. 3, p. 298 | DOI:10.1016/j.apnum.2010.10.006
  • Sulman, Mohamed; Williams, J.F.; Russell, R.D. Optimal mass transport for higher dimensional adaptive grid generation, Journal of Computational Physics, Volume 230 (2011) no. 9, p. 3302 | DOI:10.1016/j.jcp.2011.01.025
  • Xiong, Jingang; Bao, Jiguang On Jörgens, Calabi, and Pogorelov type theorem and isolated singularities of parabolic Monge–Ampère equations, Journal of Differential Equations, Volume 250 (2011) no. 1, p. 367 | DOI:10.1016/j.jde.2010.08.024
  • Jin, Qinian; Li, Aobing; Li, YanYan Estimates and existence results for a fully nonlinear Yamabe problem on manifolds with boundary, Calculus of Variations and Partial Differential Equations, Volume 28 (2007) no. 4, p. 509 | DOI:10.1007/s00526-006-0057-6

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