Regularity for convex viscosity solutions of Lagrangian mean curvature equation

References

[1] J. Bao and J. Chen, Optimal regularity for convex strong solutions of special Lagrangian equations in dimension 3, Indiana Univ. Math. J. 52 (2003), no. 5, 1231–1249. 10.1512/iumj.2003.52.2341Search in Google Scholar

[2] A. Bhattacharya, Hessian estimates for Lagrangian mean curvature equation, Calc. Var. Partial Differential Equations 60 (2021), no. 6, Paper No. 224. 10.1007/s00526-021-02097-0Search in Google Scholar

[3] A. Bhattacharya, A note on the two-dimensional Lagrangian mean curvature equation, Pacific J. Math. 318 (2022), no. 1, 43–50. 10.2140/pjm.2022.318.43Search in Google Scholar

[4] A. Bhattacharya, C. Mooney and R. Shankar, Gradient estimates for the lagrangian mean curvature equation with critical and supercritical phase, preprint (2022), https://arxiv.org/abs/2205.13096. Search in Google Scholar

[5] A. Bhattacharya and R. Shankar, Optimal regularity for lagrangian mean curvature type equations, preprint (2020), https://arxiv.org/abs/2009.04613. Search in Google Scholar

[6] L. A. Caffarelli, Interior W 2 , p estimates for solutions of the Monge–Ampère equation, Ann. of Math. (2) 131 (1990), no. 1, 135–150. 10.2307/1971510Search in Google Scholar

[7] L. A. Caffarelli and X. Cabré, Fully nonlinear elliptic equations, Amer. Math. Soc. Colloq. Publ. 43, American Mathematical Society, Providence 1995. 10.1090/coll/043Search in Google Scholar

[8] A. Chau, J. Chen and W. He, Lagrangian mean curvature flow for entire Lipschitz graphs, Calc. Var. Partial Differential Equations 44 (2012), no. 1–2, 199–220. 10.1007/s00526-011-0431-xSearch in Google Scholar

[9] J. Chen, R. Shankar and Y. Yuan, Regularity for convex viscosity solutions of special Lagrangian equation, preprint (2019), https://arxiv.org/abs/1911.05452; to appear in Comm. Pure Appl. Math. Search in Google Scholar

[10] J. Chen, M. Warren and Y. Yuan, A priori estimate for convex solutions to special Lagrangian equations and its application, Comm. Pure Appl. Math. 62 (2009), no. 4, 583–595. 10.1002/cpa.20261Search in Google Scholar

[11] F. Chiarenza, M. Frasca and P. Longo, Interior W 2 , p estimates for nondivergence elliptic equations with discontinuous coefficients, Ric. Mat. 40 (1991), no. 1, 149–168. Search in Google Scholar

[12] D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Class. Math., Springer, Berlin 2001. 10.1007/978-3-642-61798-0Search in Google Scholar

[13] R. Harvey and H. B. Lawson, Jr., Calibrated geometries, Acta Math. 148 (1982), 47–157. 10.1007/BF02392726Search in Google Scholar

[14] N. J. Hitchin, The moduli space of special Lagrangian submanifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 25 (1997), no. 3–4, 503–515. Search in Google Scholar

[15] C. Li, A compactness approach to Hessian estimates for special Lagrangian equations with supercritical phase, Nonlinear Anal. 187 (2019), 434–437. 10.1016/j.na.2019.05.006Search in Google Scholar

[16] J. G. Mealy, Calibrations on semi-Riemannian manifolds, Ph.D. thesis, Rice University, 1989. Search in Google Scholar

[17] N. Nadirashvili and S. Vlăduţ, Singular solution to special Lagrangian equations, Ann. Inst. H. Poincaré C Anal. Non Linéaire 27 (2010), no. 5, 1179–1188. 10.1016/j.anihpc.2010.05.001Search in Google Scholar

[18] T. A. Nguyen and Y. Yuan, A priori estimates for Lagrangian mean curvature flows, Int. Math. Res. Not. IMRN 2011 (2011), no. 19, 4376–4383. Search in Google Scholar

[19] A. V. Pogorelov, The Minkowski multidimensional problem, Scripta Ser. Math., V. H. Winston & Sons, Washington 1978. Search in Google Scholar

[20] R. T. Rockafellar, Convex analysis, Princeton Landmarks Math., Princeton University, Princeton 1997. Search in Google Scholar

[21] L. Simon, Lectures on geometric measure theory, Australian National University, Canberra 1983. Search in Google Scholar

[22] J. I. E. Urbas, Regularity of generalized solutions of Monge–Ampère equations, Math. Z. 197 (1988), no. 3, 365–393. 10.1007/BF01418336Search in Google Scholar

[23] C. Vitanza, W 2 , p -regularity for a class of elliptic second order equations with discontinuous coefficients, Matematiche (Catania) 47 (1992), no. 1, 177–186. Search in Google Scholar

[24] D. Wang and Y. Yuan, Singular solutions to special Lagrangian equations with subcritical phases and minimal surface systems, Amer. J. Math. 135 (2013), no. 5, 1157–1177. 10.1353/ajm.2013.0043Search in Google Scholar

[25] D. Wang and Y. Yuan, Hessian estimates for special Lagrangian equations with critical and supercritical phases in general dimensions, Amer. J. Math. 136 (2014), no. 2, 481–499. 10.1353/ajm.2014.0009Search in Google Scholar

[26] M. Warren, Special Lagrangian equations, Ph.D. thesis, University of Washington, 2008. Search in Google Scholar

[27] M. Warren, Calibrations associated to Monge–Ampère equations, Trans. Amer. Math. Soc. 362 (2010), no. 8, 3947–3962. 10.1090/S0002-9947-10-05109-3Search in Google Scholar

[28] M. Warren and Y. Yuan, Hessian estimates for the sigma-2 equation in dimension 3, Comm. Pure Appl. Math. 62 (2009), no. 3, 305–321. 10.1002/cpa.20251Search in Google Scholar

[29] M. Warren and Y. Yuan, Hessian and gradient estimates for three dimensional special Lagrangian equations with large phase, Amer. J. Math. 132 (2010), no. 3, 751–770. 10.1353/ajm.0.0115Search in Google Scholar

[30] Y. Yuan, A priori estimates for solutions of fully nonlinear special Lagrangian equations, Ann. Inst. H. Poincaré C Anal. Non Linéaire 18 (2001), no. 2, 261–270. 10.1016/s0294-1449(00)00065-2Search in Google Scholar

[31] Y. Yuan, A Bernstein problem for special Lagrangian equations, Invent. Math. 150 (2002), no. 1, 117–125. 10.1007/s00222-002-0232-0Search in Google Scholar

[32] Y. Yuan, Global solutions to special Lagrangian equations, Proc. Amer. Math. Soc. 134 (2006), no. 5, 1355–1358. 10.1090/S0002-9939-05-08081-0Search in Google Scholar