On the elliptic equation
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1985)
- Volume: 12, Issue: 2, page 191-224
- ISSN: 0391-173X
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topKenig, Carlos E., and Ni, Wei-Ming. "On the elliptic equation $Lu - k + K \exp [2u] = 0$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 12.2 (1985): 191-224. <http://eudml.org/doc/83956>.
@article{Kenig1985,
author = {Kenig, Carlos E., Ni, Wei-Ming},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {elliptic equation; degenerate elliptic operator},
language = {eng},
number = {2},
pages = {191-224},
publisher = {Scuola normale superiore},
title = {On the elliptic equation $Lu - k + K \exp [2u] = 0$},
url = {http://eudml.org/doc/83956},
volume = {12},
year = {1985},
}
TY - JOUR
AU - Kenig, Carlos E.
AU - Ni, Wei-Ming
TI - On the elliptic equation $Lu - k + K \exp [2u] = 0$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1985
PB - Scuola normale superiore
VL - 12
IS - 2
SP - 191
EP - 224
LA - eng
KW - elliptic equation; degenerate elliptic operator
UR - http://eudml.org/doc/83956
ER -
References
top- [A] L.V. Ahlfors, An extension of Schwarz's Lemma, Trans. Amer. Math. Soc., 43 (1938), pp. 359-364. Zbl0018.41002MR1501949JFM64.0315.04
- [AB] L.V. Ahlfors - L. Bers, Riemann's mapping theorem for variable metrics, Ann. of Math., 72 (1960), pp. 385-404. Zbl0104.29902MR115006
- [Av] P. Aviles, Prescribing conformal complete metrics with given positive Gaussian curvature in R2, preprint.
- [FJK] E.B. Fabes - D.S. Jerison - C.E. Kenig, The Wiener test for degenerate elliptic equations, Ann. Inst. Fourier (Grenoble), 32 (1982), pp. 151-182. Zbl0488.35034MR688024
- [FKS] E.B. Fabes - C.E. Kenig - R.P. Serapioni, The local regularity of solutions of degenerate elliptic equations, Communications in Partial Differential Equations, 7 (1982), pp. 77-116. Zbl0498.35042MR643158
- [F] A. Friedman, Bounded entire solutions of elliptic equations, Pacific J. Math., 44, (1973), pp. 497-507. Zbl0256.35024MR320506
- [Kp] L. Karp, The exterior Dirichlet problem for nonuniformly elliptic equations and applications, Workshop on Nonlinear Elliptic P.D.E., Jan. 1983MSRI, Berkeley.
- [K] J. Kazdan, Gaussian and scalar curvature, an update, Ann. of Math. Studies, 102 (S.-T. Yau, Ed.), pp. 185-192. Zbl0481.53035
- [KW] J. Kazdan - F. Warner, Curvature functions for compact 2-manifolds, Ann. of Math., 99 (1974), pp. 14-47. Zbl0273.53034MR343205
- [Kr] J.B. Keller, On solutions of Δu = f(u), Comm. Pure Appl. Math., 10 (1957), pp. 503-510. Zbl0090.31801
- [KN1] C.E. Kenig - W.-M. NI, An exterior Dirichlet problem with applications to some nonlinear equations arising in geometry, Amer. J. Math., 106 (1984), pp. 689-702. Zbl0559.35025MR745147
- [KN2] C.E. Kenig - W.-M. NI, On the elliptic equation Lu - k + K exp [2u] = 0 and conformal metrics with prescribed curvatures, Abstracts Amer. Math. Soc., 3, no. 5 (Aug. 1982), 796-35-81, p. 343.
- [KN3] C.E. Kenig - W.-M. Ni, Conformal metrics with prescribed curvatures, Abstracts Amer. Math. Soc., 4, no. 3 (April 1983), 803-35-84, p. 254.
- [LSW] W. Littman - G. Stampacchia - H. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa, Ser. III, 17 (1963), pp. 45-79. Zbl0116.30302MR161019
- [M1] R. McOwen, On the elliptic equation Δu + K exp [2u] = f and prescribed negative curvature in R2, preprint.
- [M 2] R. McOwen, Conformal metrics in R2 with prescribed Gaussian and positive total curvature, preprint.
- [N1] W.-M. Ni, On the elliptic equation Δu + K(x) exp [2u] = 0 and conformal metrics with prescribed Gaussian curvatures, Invent. Math., 66 (1982), pp. 343-352. Zbl0487.35042
- [N2] W.-M. Ni, On the elliptic equation Δu + K(x)u (n+2)/(n-2) = 0, its generalization, and applications in geometry, Indiana Univ. Math. J., 31 (1982), pp. 493-529. Zbl0496.35036
- [O] O.A. Oleinik, On the equation Δu + k(x) exp [u] = 0, Russian Math. Surveys, 33 (1978), pp. 243-244. Zbl0401.35051
- [Os] R. Osserman, On the inequality Δu ≽ f(u), Pacific J. Math., 7 (1957), pp. 1641-1647. Zbl0083.09402
- [S] D.H. Sattinger, Conformal metrics in R2 with prescribed curvature, Indiana Univ. Math. J., 22 (1972), pp. 1-4. Zbl0236.53009MR305307
- [T] G. Talenti, Elliptic equations and rearrangements, Ann. Scuola Norm. Sup., Ser. IV, 3 (1976), pp. 697-718. Zbl0341.35031MR601601
- [W] H. Wittich, Ganze Lösungen der Differentialgleichung Δu = exp [u], Math. Z., 49 (1944), pp. 579-582. Zbl0028.41001
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