Matching Tag: rellich-inequalities
Let B R B_R B R be the ball of radius R R R in R N \mathbb{R}^N R N , let N > k ≥ 2 N>k\geq 2 N > k ≥ 2 , and let u ∈ C c k ( B R ) u\in C_c^k(B_R) u ∈ C c k ( B R ) . Critical logarithmic Hardy conjecture. The inequality … holds. Moreover, the cons…
Let B R B_R B R be the ball of radius R R R in R N \mathbb{R}^N R N , let 1 < p < ∞ 1<p<\infty 1 < p < ∞ , let k ≥ 2 k\geq 2 k ≥ 2 , and let u ∈ C c k ( B R ) u\in C_c^k(B_R) u ∈ C c k ( B R ) . Write dist ( x , ∂ B R ) \operatorname{dist}(x,\partial B_R) dist ( x , ∂ B R ) for the distance from…
Let B R B_R B R be the ball of radius R R R centred at the origin in R N \mathbb{R}^N R N , let k ≥ 2 k\geq 2 k ≥ 2 , let 1 < p < N / k 1<p<N/k 1 < p < N / k , let 0 < γ ≤ ( N − k p ) / ( k p − 1 ) 0<\gamma\leq (N-kp)/(kp-1) 0 < γ ≤ ( N − k p ) / ( k p − 1 ) , and let u ∈ C c k ( B R ) u\in C_c^k(B_R) u ∈ C c k ( B R ) . Weighted hig…