Interior estimates for some semilinear elliptic problem with critical nonlinearity

Esposito, Pierpaolo

doi:10.1016/j.anihpc.2006.04.004

Esposito, Pierpaolo

Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 4, pp. 629-644.

DOI : 10.1016/j.anihpc.2006.04.004

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     author = {Esposito, Pierpaolo},
     title = {Interior estimates for some semilinear elliptic problem with critical nonlinearity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {629--644},
     publisher = {Elsevier},
     volume = {24},
     number = {4},
     year = {2007},
     doi = {10.1016/j.anihpc.2006.04.004},
     mrnumber = {2334996},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.04.004/}
}

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Esposito, Pierpaolo. Interior estimates for some semilinear elliptic problem with critical nonlinearity. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 4, pp. 629-644. doi : 10.1016/j.anihpc.2006.04.004. http://www.numdam.org/articles/10.1016/j.anihpc.2006.04.004/

Bibliographie
Cité par

[1] Adimurthi , Mancini G., Geometry and topology of the boundary in the critical Neumann problem, J. Reine Angew. Math. 456 (1994) 1-18. | MR | Zbl

[2] Adimurthi , Mancini G., The Neumann problem for elliptic equations with critical nonlinearity, in: Nonlinear Analysis, Sc. Norm. Super. di Pisa Quaderni, Scuola Norm. Sup., Pisa, 1991, pp. 9-25. | MR | Zbl

[3] Adimurthi , Mancini G., Yadava S.L., The role of the mean curvature in semilinear Neumann problem involving critical exponent, Comm. Partial Differential Equations 20 (3-4) (1995) 591-631. | Zbl

[4] Bahri A., Critical Points at Infinity in Some Variational Problems, Pitman Research Notes in Mathematics Series, vol. 182, Longman Scientific & Technical, Harlow, 1989, copublished in the United States with John Wiley & Sons, Inc., New York. | MR | Zbl

[5] Caffarelli L.A., Gidas B., Spruck J., Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (3) (1989) 271-297. | MR | Zbl

[6] Cao D., Noussair E.S., Yan S., Existence and nonexistence of interior-peaked solution for a nonlinear Neumann problem, Pacific J. Math. 200 (1) (2001) 19-41. | MR

[7] Castorina D., Mancini G., Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter, Rend. Sem. Mat. Univ. Padova 110 (2003) 147-160. | Numdam | MR | Zbl

[8] Druet O., From one bubble to several bubbles: the low-dimensional case, J. Differential Geom. 63 (3) (2003) 399-473. | MR | Zbl

[9] Druet O., Compactness for Yamabe metrics in low dimensions, Int. Math. Res. Not. 23 (2004) 1143-1191. | MR | Zbl

[10] Druet O., Hebey E., Robert F., Blow-Up Theory for Elliptic PDEs in Riemannian Geometry, Mathematical Notes, vol. 45, Princeton University Press, Princeton, NJ, 2004. | MR | Zbl

[11] Druet O., Hebey E., Robert F., A $C^{0}$ -theory for the blow-up of second order elliptic equations of critical Sobolev growth, Electron. Res. Announc. Amer. Math. Soc. 9 (2003) 19-25, (electronic). | EuDML | MR | Zbl

[12] Druet O., Hebey E., Vaugon M., Pohozaev type obstructions and solutions of bounded energy for quasilinear elliptic equations with critical Sobolev growth. The conformally flat case, Nonlinear Anal. 51 (1) (2002) 79-94. | MR | Zbl

[13] Ghoussoub N., Gui C., Zhu M., On a singularly perturbed Neumann problem with the critical exponent, Comm. Partial Differential Equations 26 (11-12) (2001) 1929-1946. | MR | Zbl

[14] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, second ed., Springer-Verlag, 1983. | MR | Zbl

[15] Gui C., Lin C.S., Estimates for boundary-bubbling solutions to an elliptic Neumann problem, J. Reine Angew. Math. 546 (2002) 201-235. | MR | Zbl

[16] Li Y.Y., Prescribing scalar curvature on $S^{n}$ and related problems. I, J. Differential Equations 120 (2) (1995) 319-410. | MR | Zbl

[17] Lin C.S., Ni W.M., Takagi I., Large amplitude stationary solutions to a chemotaxis system, J. Differential Equations 72 (1) (1988) 1-27. | MR | Zbl

[18] Meinhardt H., Models of Biological Pattern Formation, Academic Press, London, 1982.

[19] Pohozaev S.I., Eigenfunctions of the equation $Δ u + λ f (u) = 0$ , Soviet Math. Dokl. 6 (1965) 1408-1411, Translated from the, Russ. Dokl. Acad. Nauk SSSR 165 (1965) 33-36. | MR | Zbl

[20] Rey O., The question of interior blow-up points for an elliptic Neumann problem: the critical case, J. Math. Pures Appl. (9) 81 (7) (2002) 655-696. | MR | Zbl

[21] Rey O., Boundary effect for an elliptic Neumann problem with critical nonlinearity, Comm. Partial Differential Equations 22 (7-8) (1997). | MR | Zbl

[22] Schoen R., On the number of constant scalar curvature metrics in a conformal class, in: Differential Geometry, Pitman Monogr. Surveys Pure Appl. Math., vol. 52, Longman Sci. Tech., Harlow, 1991, pp. 311-320. | MR | Zbl

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