Geodesic
Sharp a priori estimates for a quasilinear degenerate elliptic problem
Sbornik. Mathematics, Tome 79 (1994) no. 2, pp. 335-346 Cet article a éte moissonné depuis la source Math-Net.Ru

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A study is made of the equation $$ \Delta u+\frac1{|x|^\gamma }|u|^{p-2}u=h(x) $$ in a bounded domain $\Omega\subset\mathbb{R}^N$ $(N\ge3)$ with homogeneous Dirichlet boundary conditions. Here $2 and $2\gamma>2N-(N-2)p$. Sharp best possible a priori estimates are established for the solution of this problem and for its first and second derivatives in the corresponding function spaces. 
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     author = {S. I. Pokhozhaev},
     title = {Sharp a~priori estimates for a~quasilinear degenerate elliptic problem},
     journal = {Sbornik. Mathematics},
     pages = {335--346},
     year = {1994},
     volume = {79},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_79_2_a5/}
}
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S. I. Pokhozhaev. Sharp a priori estimates for a quasilinear degenerate elliptic problem. Sbornik. Mathematics, Tome 79 (1994) no. 2, pp. 335-346. http://geodesic.mathdoc.fr/item/SM_1994_79_2_a5/

[1] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR

[2] Gilbarg D., Tridinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR | Zbl

[3] Pokhozhaev S. I., “O sobstvennykh funktsiyakh uravneniya $\Delta u+\lambda f(u)=0 $”, DAN SSSR, 165:1 (1965), 36–39 | MR | Zbl

[4] Agmon S., Duglis A., Nirenberg L., Otsenki reshenii ellipticheskikh uravnenii vblizi granitsy, IL, M., 1962

[5] Berestycki H., Lions P.-L., “Nonlinear scalar field equations. I: Existence of a ground state”, Arch. Rat. Mech. Anal., 82:4 (1983), 313–345 | MR | Zbl