Interior estimates for some semilinear elliptic problem with critical nonlinearity
Annales de l'I.H.P. Analyse non linéaire, Volume 24 (2007) no. 4, p. 629-644
@article{AIHPC_2007__24_4_629_0,
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},
publisher = {Elsevier},
volume = {24},
number = {4},
year = {2007},
pages = {629-644},
doi = {10.1016/j.anihpc.2006.04.004},
zbl = {pre05181995},
mrnumber = {2334996},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2007__24_4_629_0}
}

Esposito, Pierpaolo. Interior estimates for some semilinear elliptic problem with critical nonlinearity. Annales de l'I.H.P. Analyse non linéaire, Volume 24 (2007) no. 4, pp. 629-644. doi : 10.1016/j.anihpc.2006.04.004. http://www.numdam.org/item/AIHPC_2007__24_4_629_0/

[1] Adimurthi , Mancini G., Geometry and topology of the boundary in the critical Neumann problem, J. Reine Angew. Math. 456 (1994) 1-18. | MR 1301449 | Zbl 0804.35036

[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 1205370 | Zbl 0836.35048

[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 0847.35047

[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 1019828 | Zbl 0676.58021

[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 982351 | Zbl 0702.35085

[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 1863405 | Zbl pre01818894

[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 2033005 | Zbl 1121.35053

[8] Druet O., From one bubble to several bubbles: the low-dimensional case, J. Differential Geom. 63 (3) (2003) 399-473. | MR 2015469 | Zbl 1070.53017

[9] Druet O., Compactness for Yamabe metrics in low dimensions, Int. Math. Res. Not. 23 (2004) 1143-1191. | MR 2041549 | Zbl 1085.53029

[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 2063399 | Zbl 1059.58017

[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). | MR 1988868 | Zbl 1061.58020

[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 1915742 | Zbl 1066.35032

[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 1876408 | Zbl 0997.35021

[14] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, second ed., Springer-Verlag, 1983. | MR 737190 | Zbl 0562.35001

[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 1900999 | Zbl 1136.35380 | Zbl pre01738273

[16] Li Y.Y., Prescribing scalar curvature on ${S}^{n}$ and related problems. I, J. Differential Equations 120 (2) (1995) 319-410. | MR 1347349 | Zbl 0827.53039

[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 929196 | Zbl 0676.35030

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

[19] Pohozaev S.I., Eigenfunctions of the equation $\Delta u+\lambda f\left(u\right)=0$, Soviet Math. Dokl. 6 (1965) 1408-1411, Translated from the, Russ. Dokl. Acad. Nauk SSSR 165 (1965) 33-36. | MR 192184 | Zbl 0141.30202

[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 1968337 | Zbl 1066.35033

[21] Rey O., Boundary effect for an elliptic Neumann problem with critical nonlinearity, Comm. Partial Differential Equations 22 (7-8) (1997). | MR 1466311 | Zbl 0891.35040

[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 1173050 | Zbl 0733.53021