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Nonautonomous bifurcation of bounded solutions II: A Shovel-Bifurcation pattern
A Harnack inequality for fractional Laplace equations with lower order terms
1. | Departamento de Matemática, Universidad Técnica Federico Santa María, Avda. España 1680, Valparaíso, Chile |
2. | School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China |
References:
[1] |
R. F. Bass and D. A. Levin, Harnack inequalities for jump processes, Potential Anal., 17 (2002), 375-388
doi: 10.1023/A:1016378210944. |
[2] |
X. Cabre and Y. Sire, Nonlinear equations for fractional laplacians I: Regularity, maximum principles, and hamiltonian estimates, preprint, arXiv:1012.0867v1. |
[3] |
L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations, 32 (2007), 1245-1260. |
[4] |
Z.-Q. Chen and R. Song, Estimates on Green functions and Poisson kernels for symmetric stable processes, Math. Ann., 312 (1998), 465-501.
doi: 10.1007/s002080050232. |
[5] |
E. Fabes, C. Kenig and R. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations, 7 (1982), 77-116. |
[6] |
Q. Han and F.-H. Lin, "Elliptic Partial Differential Equations," Courant Lecture Notes in Mathematics, 1, New York University, Courant Institute of Mathematical Sciences, New York, American Mathematical Society, Providence, RI, 1997. |
[7] |
Z.-C. Han and Y. Y. Li, The Yamabe problem on manifolds with boundary: Existence and compactness results, Duke Math. J., 99 (1999), 489-542.
doi: 10.1215/S0012-7094-99-09916-7. |
[8] |
F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math., 14 (1961), 415-426.
doi: 10.1002/cpa.3160140317. |
[9] |
M. Kassmann, The classical Harnack inequality fails for non-local operators, preprint. |
[10] |
B. Muckenhoupt and R. Wheeden, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc., 192 (1974), 261-274.
doi: 10.1090/S0002-9947-1974-0340523-6. |
[11] |
E. Stein, "Singular Integrals and Differentiability Properties of Function," Princeton Mathematical Series, 30, Princeton University Press, Princeton, NJ, 1970. |
show all references
References:
[1] |
R. F. Bass and D. A. Levin, Harnack inequalities for jump processes, Potential Anal., 17 (2002), 375-388
doi: 10.1023/A:1016378210944. |
[2] |
X. Cabre and Y. Sire, Nonlinear equations for fractional laplacians I: Regularity, maximum principles, and hamiltonian estimates, preprint, arXiv:1012.0867v1. |
[3] |
L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations, 32 (2007), 1245-1260. |
[4] |
Z.-Q. Chen and R. Song, Estimates on Green functions and Poisson kernels for symmetric stable processes, Math. Ann., 312 (1998), 465-501.
doi: 10.1007/s002080050232. |
[5] |
E. Fabes, C. Kenig and R. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations, 7 (1982), 77-116. |
[6] |
Q. Han and F.-H. Lin, "Elliptic Partial Differential Equations," Courant Lecture Notes in Mathematics, 1, New York University, Courant Institute of Mathematical Sciences, New York, American Mathematical Society, Providence, RI, 1997. |
[7] |
Z.-C. Han and Y. Y. Li, The Yamabe problem on manifolds with boundary: Existence and compactness results, Duke Math. J., 99 (1999), 489-542.
doi: 10.1215/S0012-7094-99-09916-7. |
[8] |
F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math., 14 (1961), 415-426.
doi: 10.1002/cpa.3160140317. |
[9] |
M. Kassmann, The classical Harnack inequality fails for non-local operators, preprint. |
[10] |
B. Muckenhoupt and R. Wheeden, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc., 192 (1974), 261-274.
doi: 10.1090/S0002-9947-1974-0340523-6. |
[11] |
E. Stein, "Singular Integrals and Differentiability Properties of Function," Princeton Mathematical Series, 30, Princeton University Press, Princeton, NJ, 1970. |
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