Analytical approach of the symmetry: Sharp supercritical Hardy-Sobolev inequalities and applications

作者：Cotsiolis Athanase; Labropoulos Nikos^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2018, 171: 134-155.

DOI：10.1016/j.na.2018.02.005

• Analytical approach of the symmetry
• Supercritical Hardy-Sobolev inequalities
• Supercritical Hardy-Sobolev elliptic equations

We consider the optimal Hardy-Sobolev inequality on smooth bounded symmetric domains of the Euclidean space without any assumption concerning the "shape" of the boundary (i.e. some convexity) confirming that the symmetry of a domain is an intrinsic property characterizing both the domain itself and its boundary. Our model domain is the solid torus because of its particular interest in terms both of the geometry and of the analysis. We apply the results of the above study to solve the supercritical problem
(P) Delta(p)u + a(x)u(p-1) = f(x) u(p)*((s)-1)/vertical bar x vertical bar(s), u > 0 on T, u = 0 on partial derivative T,
1 < p < 2, 0 <= s <= p and p* (s) = p(2 - s)/2 - p
and some variants of it.

• 出版日期2018-6