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Interpolation by linear programming I
Fundamental solutions for a class of Isaacs integral operators
1. | Departamento de Ingeneria Matematica F.C.F.M., Universidad de Chile, Casilla 170 Correro 3, Santiago |
2. | Departamento de Matemática, Universidad Técnico Fedrico Santa María, Avenida España 1680, Casilla 110-V, Valparaíso |
References:
[1] |
S. Armstrong and B. Sirakov, Sharp Liouville results for Fully Nonlinear equations with power-growth nonlinearities, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (2010) to appear. |
[2] |
S. Armstrong, B. Sirakov and C. Smart, Fundamental solutions of fully nonlinear elliptic equations, Communications on Pure and Applied Mathematics (2011) to appear. |
[3] |
X. Cabré and L. Caffarelli, "Fully Nonlinear Elliptic Equation," American Mathematical Society, Colloquium Publication, Vol. 43, 1995. |
[4] |
L. Caffarelli and L. Silvestre, Regularity theory for fully nonlinear integro-differential equations, Comm. Pure Appl. Math., 62 (2009), 597-638. |
[5] |
L. Caffarelli, B. Gidas and J. Spruck, Asymptotic symmetry and local behavior of semi-linear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42, 3 (1989), 271-297.
doi: 10.1002/cpa.3160420304. |
[6] |
I. Capuzzo-Dolcetta and A. Cutri, Hadamard and Liouville type results for fully nonlinear partial differential inequalities, Communications in Contemporary Mathematics, 3 (2003), 435-448.
doi: 10.1142/S0219199703001014. |
[7] |
W. Chen and C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. Journal, 3 (1991), 615-622. |
[8] |
W. Chen, C. Li and B. Ou, Classification of solutions for a system of integral equations, Comm. PDE, 30 (2005), 59-65.
doi: 10.1081/PDE-200044445. |
[9] |
A. Cutri and F. Leoni, On the Liouville property for fully nonlinear equations, Ann. Inst. H. Poincaré Analyse non lineaire, 17 (2000), 219-245. |
[10] |
P. Felmer and A. Quaas, Critical exponents for uniformly elliptic extremal operators, Indiana Univ. Math. J., 55 (2006), 593-629.
doi: 10.1512/iumj.2006.55.2864. |
[11] |
P. Felmer, A. Quaas, Fundamental solutions and two properties of elliptic maximal and minimal operators, Trans. Amer. Math. Soc., 361 (2009), 5721-5736.
doi: 10.1090/S0002-9947-09-04566-8. |
[12] |
P. Felmer and A. Quaas, Fundamental solutions and Liouville type properties for nonlinear integral operators, Advances in Mathematics, 226 (2011), 2712-2738.
doi: 10.1016/j.aim.2010.09.023. |
[13] |
B. Gidas, Symmetry and isolated singularitiesof positive solutions of nonlinear elliptic equations, Nonlinear partial differential equations in engineering and applied science (Proc. Conf., Univ. Rhode Island, Kingston, R.I., 1979), pp. 255-273, Lecture Notes in Pure and Appl. Math., 54, Dekker, New York, 1980. |
[14] |
B. Gidas and J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math., 34 (1981), 525-598.
doi: 10.1002/cpa.3160340406. |
[15] |
D. Labutin, Removable singularities for fully nonlinear elliptic equations, Arch. Rational Mech. Anal., 155 (2000), 201-214.
doi: 10.1007/s002050000108. |
[16] |
D. Labutin, Isolated singularities for fully nonlinear elliptic equations, Journal of Differential Equation, 177 (2001), 49-76.
doi: 10.1006/jdeq.2001.3998. |
[17] |
Y. Y. Li, Remark on some conformally invariant integral equations: The method of moving spheres, J. Eur. Math. Soc., 6 (2004), 153-180.
doi: 10.4171/JEMS/6. |
show all references
References:
[1] |
S. Armstrong and B. Sirakov, Sharp Liouville results for Fully Nonlinear equations with power-growth nonlinearities, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (2010) to appear. |
[2] |
S. Armstrong, B. Sirakov and C. Smart, Fundamental solutions of fully nonlinear elliptic equations, Communications on Pure and Applied Mathematics (2011) to appear. |
[3] |
X. Cabré and L. Caffarelli, "Fully Nonlinear Elliptic Equation," American Mathematical Society, Colloquium Publication, Vol. 43, 1995. |
[4] |
L. Caffarelli and L. Silvestre, Regularity theory for fully nonlinear integro-differential equations, Comm. Pure Appl. Math., 62 (2009), 597-638. |
[5] |
L. Caffarelli, B. Gidas and J. Spruck, Asymptotic symmetry and local behavior of semi-linear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42, 3 (1989), 271-297.
doi: 10.1002/cpa.3160420304. |
[6] |
I. Capuzzo-Dolcetta and A. Cutri, Hadamard and Liouville type results for fully nonlinear partial differential inequalities, Communications in Contemporary Mathematics, 3 (2003), 435-448.
doi: 10.1142/S0219199703001014. |
[7] |
W. Chen and C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. Journal, 3 (1991), 615-622. |
[8] |
W. Chen, C. Li and B. Ou, Classification of solutions for a system of integral equations, Comm. PDE, 30 (2005), 59-65.
doi: 10.1081/PDE-200044445. |
[9] |
A. Cutri and F. Leoni, On the Liouville property for fully nonlinear equations, Ann. Inst. H. Poincaré Analyse non lineaire, 17 (2000), 219-245. |
[10] |
P. Felmer and A. Quaas, Critical exponents for uniformly elliptic extremal operators, Indiana Univ. Math. J., 55 (2006), 593-629.
doi: 10.1512/iumj.2006.55.2864. |
[11] |
P. Felmer, A. Quaas, Fundamental solutions and two properties of elliptic maximal and minimal operators, Trans. Amer. Math. Soc., 361 (2009), 5721-5736.
doi: 10.1090/S0002-9947-09-04566-8. |
[12] |
P. Felmer and A. Quaas, Fundamental solutions and Liouville type properties for nonlinear integral operators, Advances in Mathematics, 226 (2011), 2712-2738.
doi: 10.1016/j.aim.2010.09.023. |
[13] |
B. Gidas, Symmetry and isolated singularitiesof positive solutions of nonlinear elliptic equations, Nonlinear partial differential equations in engineering and applied science (Proc. Conf., Univ. Rhode Island, Kingston, R.I., 1979), pp. 255-273, Lecture Notes in Pure and Appl. Math., 54, Dekker, New York, 1980. |
[14] |
B. Gidas and J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math., 34 (1981), 525-598.
doi: 10.1002/cpa.3160340406. |
[15] |
D. Labutin, Removable singularities for fully nonlinear elliptic equations, Arch. Rational Mech. Anal., 155 (2000), 201-214.
doi: 10.1007/s002050000108. |
[16] |
D. Labutin, Isolated singularities for fully nonlinear elliptic equations, Journal of Differential Equation, 177 (2001), 49-76.
doi: 10.1006/jdeq.2001.3998. |
[17] |
Y. Y. Li, Remark on some conformally invariant integral equations: The method of moving spheres, J. Eur. Math. Soc., 6 (2004), 153-180.
doi: 10.4171/JEMS/6. |
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