Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899429 | Journal of Mathematical Analysis and Applications | 2018 | 16 Pages |
Abstract
We consider the Hardy inequality in canonical doubly connected plane domains. For any annulus A we determine sharp Hardy's constant c2(A) in function of conformal modulus M(A). Namely, for any annulus A with fixed conformal modulus M(A)=M we prove thatc2(A)={1/4,if Mâ(0,Mâ];γ(2âγ)/4,if Mâ(Mâ,â), where γ=γ(M)â(1,2). The critical modulus Mââ0.57298 and the values of γ(M) are found as roots of certain equations, containing the Gauss hypergeometric functions. In particular, we show that the sharp Hardy constants c2(A) depend on M continuously and that they tend to zero as Mââ. In addition, we describe an application of results to a Rellich type inequality.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
F.G. Avkhadiev,