Regularity of Degenerate Monge–Ampère and Prescribed Gaussian Curvature Equations in Two Dimensions

Potential Analysis ◽

10.1007/s11118-005-0915-4 ◽

2006 ◽

Vol 24 (3) ◽

pp. 267-301 ◽

Author(s):

Eric T. Sawyer ◽

Richard L. Wheeden

Keyword(s):

Gaussian Curvature ◽

Two Dimensions ◽

Prescribed Gaussian Curvature ◽

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Hypersurfaces in IRn+1with prescribed gaussian curvature and related equations of monge—ampére type

Communications in Partial Differential Equations ◽

10.1080/03605308408820348 ◽

1984 ◽

Vol 9 (8) ◽

pp. 807-838 ◽

Author(s):

V.I. Oliker

Keyword(s):

Gaussian Curvature ◽

Prescribed Gaussian Curvature ◽

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Compactness issues and bubbling phenomena for the prescribed Gaussian curvature equation on the torus

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-015-0872-8 ◽

2015 ◽

Vol 54 (3) ◽

pp. 2483-2501 ◽

Author(s):

Luca Galimberti

Keyword(s):

Gaussian Curvature ◽

Curvature Equation ◽

Prescribed Gaussian Curvature ◽

Bubbling Phenomena

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Monge–Ampére simulation of fourth order PDEs in two dimensions with application to elastic–electrostatic contact problems

Journal of Computational Physics ◽

10.1016/j.jcp.2017.08.032 ◽

2017 ◽

Vol 349 ◽

pp. 328-350 ◽

Author(s):

Kelsey L. DiPietro ◽

Alan E. Lindsay

Keyword(s):

Fourth Order ◽

Contact Problems ◽

Two Dimensions ◽

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A priori estimates for quasilinear equations related to the Monge-Ampère equation in two dimensions

Journal d Analyse Mathématique ◽

10.1007/bf02807409 ◽

2005 ◽

Vol 97 (1) ◽

pp. 257-316 ◽

Author(s):

Eric T. Sawyer ◽

Richard L. Wheeden

Keyword(s):

A Priori Estimates ◽

A Priori ◽

Two Dimensions ◽

Quasilinear Equations ◽

Priori Estimates ◽

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Compactness results for immersions of prescribed Gaussian curvature I – analytic aspects

Advances in Mathematics ◽

10.1016/j.aim.2011.10.008 ◽

2012 ◽

Vol 229 (2) ◽

pp. 731-769 ◽

Author(s):

Graham Smith

Keyword(s):

Gaussian Curvature ◽

Prescribed Gaussian Curvature

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Compactness for immersions of prescribed Gaussian curvature II: geometric aspects

Geometriae Dedicata ◽

10.1007/s10711-013-9921-7 ◽

2014 ◽

Vol 172 (1) ◽

pp. 303-350 ◽

Author(s):

Graham Smith

Keyword(s):

Gaussian Curvature ◽

Prescribed Gaussian Curvature

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Timelike surfaces in the Lorentz–Minkowski space with prescribed Gaussian curvature and Gauss map

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2005.07.004 ◽

2006 ◽

Vol 56 (8) ◽

pp. 1357-1369 ◽

Author(s):

Juan A. Aledo ◽

José M. Espinar ◽

José A. Gálvez

Keyword(s):

Minkowski Space ◽

Gaussian Curvature ◽

Gauss Map ◽

Prescribed Gaussian Curvature

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Riemannian structures of prescribed Gaussian curvature for compact 2-manifolds

Journal of Differential Geometry ◽

10.4310/jdg/1214429996 ◽

1971 ◽

Vol 5 (3-4) ◽

pp. 325-332 ◽

Author(s):

Melvyn S. Berger

Keyword(s):

Gaussian Curvature ◽

Prescribed Gaussian Curvature

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Monge-Ampère equations and surfaces with negative Gaussian curvature

Banach Center Publications ◽

10.4064/-39-1-161-170 ◽

1997 ◽

Vol 39 (1) ◽

pp. 161-170 ◽

Author(s):

Mikio Tsuji

Keyword(s):

Gaussian Curvature ◽

Negative Gaussian Curvature ◽

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Convex integration for the Monge–Ampère equation in two dimensions

Analysis & PDE ◽

10.2140/apde.2017.10.695 ◽

2017 ◽

Vol 10 (3) ◽

pp. 695-727 ◽

Author(s):

Marta Lewicka ◽

Mohammad Reza Pakzad

Keyword(s):

Two Dimensions ◽

Convex Integration ◽

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