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A note on the unique continuation property for fully nonlinear elliptic equations
1. | Department of Mathematics, University of California, Irvine, CA 92697, United States |
References:
[1] |
V. Adolfsson and L. Escauriaza, $C^{1, \alpha}$ domains and unique continuation at the boundary, Comm. Pure Appl. Math., 50 (1997), 935-969.
doi: 10.1002/(SICI)1097-0312(199710)50:10<935::AID-CPA1>3.0.CO;2-H. |
[2] |
N. Aronszajn, A. Krzywicki and J. Szarski, A unique continuation theorem for exterior differential forms on Riemannian manifolds, Ark. Mat., 4 (1962), 417-453. |
[3] |
S. N. Armstrong and L. Silvestre, Unique continuation for fully nonlinear elliptic equations, Math. Res. Lett., 18 (2011), 921-926.
doi: 10.4310/MRL.2011.v18.n5.a9. |
[4] |
X. Cabre and L. Caffarelli, Fully Nonlinear Elliptic Equations, Volume 43 of American Mathematical Society Colloquium Publications. 43 American Mathematical Society, Providence, RI, (1995). vi+104 pp. ISBN: 0-8218-0437-5. |
[5] |
N. Garofalo and F. Lin, Monotonicity properties of variational integrals, $A_p$ weights and unique continuation, Indiana Univ. Math. J., 35 (1986), 245-268.
doi: 10.1512/iumj.1986.35.35015. |
[6] |
N. Garofalo and F. Lin, Unique continuation for elliptic operators: a geometric-variational approach, Comm. Pure Appl. Math., 40 (1987), 347-366.
doi: 10.1002/cpa.3160400305. |
[7] |
I. Kukavica and K. Nystrom, Unique continuation at the boundary for Dini domains, Proc. Amer. Math. Soc., 126 (1998), 441-446.
doi: 10.1090/S0002-9939-98-04065-9. |
[8] |
G. Lieberman, Second Order Parabolic Differential Equations, World Scientific Publishing Co., Inc., River Edge, NJ,(1996). xii+439 pp. ISBN: 981-02-2883-X
doi: 10.1142/3302. |
[9] |
N. Nadirashvili and S. Vlădut, Singular solutions of Hessian fully nonlinear elliptic equations, Adv. Math., 228 (2011), 1718-1741.
doi: 10.1016/j.aim.2011.06.030. |
[10] |
O. Savin, Small perturbation solutions for elliptic equations, Comm. Partial Differential Equations, 32 (2007), 557-578.
doi: 10.1080/03605300500394405. |
[11] |
L. Silvestre and B. Sirakov, Boundary regularity for viscosity solutions of fully nonlinear elliptic equations, http://arxiv.org/pdf/1306.6672.pdf.
doi: 10.1080/03605302.2013.842249. |
show all references
References:
[1] |
V. Adolfsson and L. Escauriaza, $C^{1, \alpha}$ domains and unique continuation at the boundary, Comm. Pure Appl. Math., 50 (1997), 935-969.
doi: 10.1002/(SICI)1097-0312(199710)50:10<935::AID-CPA1>3.0.CO;2-H. |
[2] |
N. Aronszajn, A. Krzywicki and J. Szarski, A unique continuation theorem for exterior differential forms on Riemannian manifolds, Ark. Mat., 4 (1962), 417-453. |
[3] |
S. N. Armstrong and L. Silvestre, Unique continuation for fully nonlinear elliptic equations, Math. Res. Lett., 18 (2011), 921-926.
doi: 10.4310/MRL.2011.v18.n5.a9. |
[4] |
X. Cabre and L. Caffarelli, Fully Nonlinear Elliptic Equations, Volume 43 of American Mathematical Society Colloquium Publications. 43 American Mathematical Society, Providence, RI, (1995). vi+104 pp. ISBN: 0-8218-0437-5. |
[5] |
N. Garofalo and F. Lin, Monotonicity properties of variational integrals, $A_p$ weights and unique continuation, Indiana Univ. Math. J., 35 (1986), 245-268.
doi: 10.1512/iumj.1986.35.35015. |
[6] |
N. Garofalo and F. Lin, Unique continuation for elliptic operators: a geometric-variational approach, Comm. Pure Appl. Math., 40 (1987), 347-366.
doi: 10.1002/cpa.3160400305. |
[7] |
I. Kukavica and K. Nystrom, Unique continuation at the boundary for Dini domains, Proc. Amer. Math. Soc., 126 (1998), 441-446.
doi: 10.1090/S0002-9939-98-04065-9. |
[8] |
G. Lieberman, Second Order Parabolic Differential Equations, World Scientific Publishing Co., Inc., River Edge, NJ,(1996). xii+439 pp. ISBN: 981-02-2883-X
doi: 10.1142/3302. |
[9] |
N. Nadirashvili and S. Vlădut, Singular solutions of Hessian fully nonlinear elliptic equations, Adv. Math., 228 (2011), 1718-1741.
doi: 10.1016/j.aim.2011.06.030. |
[10] |
O. Savin, Small perturbation solutions for elliptic equations, Comm. Partial Differential Equations, 32 (2007), 557-578.
doi: 10.1080/03605300500394405. |
[11] |
L. Silvestre and B. Sirakov, Boundary regularity for viscosity solutions of fully nonlinear elliptic equations, http://arxiv.org/pdf/1306.6672.pdf.
doi: 10.1080/03605302.2013.842249. |
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