Interior estimates for some semilinear elliptic problem with critical nonlinearity

 Access to full text

 Full (PDF)

1. [1] Adimurthi, Mancini G., Geometry and topology of the boundary in the critical Neumann problem, J. Reine Angew. Math.456 (1994) 1-18. Zbl0804.35036MR1301449
2. [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. Zbl0836.35048MR1205370
3. [3] Adimurthi, Mancini G., Yadava S.L., The role of the mean curvature in semilinear Neumann problem involving critical exponent, Comm. Partial Differential Equations20 (3–4) (1995) 591-631. Zbl0847.35047
4. [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. Zbl0676.58021MR1019828
5. [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. Zbl0702.35085MR982351
6. [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. Zbl1140.35440MR1863405
7. [7] Castorina D., Mancini G., Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter, Rend. Sem. Mat. Univ. Padova110 (2003) 147-160. Zbl1121.35053MR2033005
8. [8] Druet O., From one bubble to several bubbles: the low-dimensional case, J. Differential Geom.63 (3) (2003) 399-473. Zbl1070.53017MR2015469
9. [9] Druet O., Compactness for Yamabe metrics in low dimensions, Int. Math. Res. Not.23 (2004) 1143-1191. Zbl1085.53029MR2041549
10. [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. Zbl1059.58017MR2063399
11. [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). Zbl1061.58020MR1988868
12. [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. Zbl1066.35032MR1915742
13. [13] Ghoussoub N., Gui C., Zhu M., On a singularly perturbed Neumann problem with the critical exponent, Comm. Partial Differential Equations26 (11–12) (2001) 1929-1946. Zbl0997.35021
14. [14] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, second ed., Springer-Verlag, 1983. Zbl0562.35001MR737190
15. [15] Gui C., Lin C.S., Estimates for boundary-bubbling solutions to an elliptic Neumann problem, J. Reine Angew. Math.546 (2002) 201-235. Zbl1136.35380MR1900999
16. [16] Li Y.Y., Prescribing scalar curvature on $S^n$ and related problems. I, J. Differential Equations120 (2) (1995) 319-410. Zbl0827.53039MR1347349
17. [17] Lin C.S., Ni W.M., Takagi I., Large amplitude stationary solutions to a chemotaxis system, J. Differential Equations72 (1) (1988) 1-27. Zbl0676.35030MR929196
18. [18] Meinhardt H., Models of Biological Pattern Formation, Academic Press, London, 1982. 
19. [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 SSSR165 (1965) 33-36. Zbl0141.30202MR192184
20. [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. Zbl1066.35033MR1968337
21. [21] Rey O., Boundary effect for an elliptic Neumann problem with critical nonlinearity, Comm. Partial Differential Equations22 (7–8) (1997). Zbl0891.35040
22. [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. Zbl0733.53021MR1173050