Remarks on a Sobolev–Hardy inequality
نویسنده
چکیده
where x = (y, z) ∈ R × R was studied by Badiale and Tarantello in [1]. Our aim is to solve two open problems contained in [1]. First we compute the optimal value of the constant C in Equation (1) in the case of Hardy’s inequality, namely p = q = β. In fact we prove a more general inequality with optimal constant in Section 2. In Section 3, we consider the symmetry of the optimal functions. Using the “product” of two symmetrizations, we prove that the optimal functions depend only on (|y|, |z|).
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تاریخ انتشار 2002