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Rotating periodic solutions of second order dissipative dynamical systems
Smooth local solutions to Weingarten equations and $\sigma_k$-equations
1. | Department of Mathematics, University of California, Santa Barbara, CA 93106, United States |
2. | Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, United States |
References:
[1] |
L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear second-order elliptic equations, IV. Starshaped compact Weingarten hypersurfaces,, Current topics in partial differential equations, (1986), 1.
|
[2] |
L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear second-order elliptic equations V. The Dirichlet problem for Weingarten Hypersurfaces,, Comm. Pure Appl. Math., 41 (1988), 47.
doi: 10.1002/cpa.3160410105. |
[3] |
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order,, 3rd ed., (2001).
|
[4] |
Q. Han, On the isometric embedding of surfaces with Gauss curvature changing sign cleanly,, Comm. Pure Appl. Math., 58 (2005), 285.
doi: 10.1002/cpa.20054. |
[5] |
Q. Han, Local solutions to a class of Monge-Ampère equations of the mixed type,, Duke Math. J., 136 (2007), 421.
|
[6] |
Q. Han, J.-X. Hong and C.-S. Lin, Local isometric embedding of surfaces with nonpositive gaussian curvature,, J. Diff. Geometry, 63 (2003), 475.
|
[7] |
J.-X. Hong and C. Zuily, Existence of $C^\infty$ local solutions for the Monge-Ampère equation,, Invent. Math., 89 (1987), 645.
doi: 10.1007/BF01388988. |
[8] |
C.-S. Lin, The local isometric embedding in $\mathbbR^3$ of 2-dimensional Riemannian manifolds with nonnegative curvature,, J. Diff. Geometry, 21 (1985), 213.
|
[9] |
C.-S. Lin, The local isometric embedding in $\mathbbR^3$ of two dimensional Riemannian manifolds with Gaussian curvature changing sign clearly,, Comm. Pure Appl. Math., 39 (1986), 867.
doi: 10.1002/cpa.3160390607. |
[10] |
W.-M. Sheng, N. Trudinger and X.-J. Wang, Prescribed Weingarten curvature equations,, Recent Development in Geometry and Analysis, 23 (2012), 359.
|
[11] |
X.-J. Wang, The $k$-Hessian equation,, Geometric analysis and PDEs, (1977), 177.
doi: 10.1007/978-3-642-01674-5_5. |
show all references
References:
[1] |
L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear second-order elliptic equations, IV. Starshaped compact Weingarten hypersurfaces,, Current topics in partial differential equations, (1986), 1.
|
[2] |
L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear second-order elliptic equations V. The Dirichlet problem for Weingarten Hypersurfaces,, Comm. Pure Appl. Math., 41 (1988), 47.
doi: 10.1002/cpa.3160410105. |
[3] |
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order,, 3rd ed., (2001).
|
[4] |
Q. Han, On the isometric embedding of surfaces with Gauss curvature changing sign cleanly,, Comm. Pure Appl. Math., 58 (2005), 285.
doi: 10.1002/cpa.20054. |
[5] |
Q. Han, Local solutions to a class of Monge-Ampère equations of the mixed type,, Duke Math. J., 136 (2007), 421.
|
[6] |
Q. Han, J.-X. Hong and C.-S. Lin, Local isometric embedding of surfaces with nonpositive gaussian curvature,, J. Diff. Geometry, 63 (2003), 475.
|
[7] |
J.-X. Hong and C. Zuily, Existence of $C^\infty$ local solutions for the Monge-Ampère equation,, Invent. Math., 89 (1987), 645.
doi: 10.1007/BF01388988. |
[8] |
C.-S. Lin, The local isometric embedding in $\mathbbR^3$ of 2-dimensional Riemannian manifolds with nonnegative curvature,, J. Diff. Geometry, 21 (1985), 213.
|
[9] |
C.-S. Lin, The local isometric embedding in $\mathbbR^3$ of two dimensional Riemannian manifolds with Gaussian curvature changing sign clearly,, Comm. Pure Appl. Math., 39 (1986), 867.
doi: 10.1002/cpa.3160390607. |
[10] |
W.-M. Sheng, N. Trudinger and X.-J. Wang, Prescribed Weingarten curvature equations,, Recent Development in Geometry and Analysis, 23 (2012), 359.
|
[11] |
X.-J. Wang, The $k$-Hessian equation,, Geometric analysis and PDEs, (1977), 177.
doi: 10.1007/978-3-642-01674-5_5. |
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