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- W1973911476 abstract "In this paper we establish the boundedness of the extremal solution u∗ in dimension N=4 of the semilinear elliptic equation −Δu=λf(u), in a general smooth bounded domain Ω⊂RN, with Dirichlet data u|∂Ω=0, where f is a C1 positive, nondecreasing and convex function in [0,∞) such that f(s)/s→∞ as s→∞. In addition, we prove that, for N≥5, the extremal solution u∗∈W2,NN−2. This gives u∗∈LNN−4, if N≥5 and u∗∈H01, if N=6." @default.
- W1973911476 created "2016-06-24" @default.
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- W1973911476 date "2013-03-01" @default.
- W1973911476 modified "2023-10-13" @default.
- W1973911476 title "Boundedness of extremal solutions in dimension 4" @default.
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- W1973911476 doi "https://doi.org/10.1016/j.aim.2012.11.015" @default.
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