Via the variational methods, we prove the existence of a nontrivial solution to a singular semilinear elliptic equation with critical Sobolev-Hardy exponent under certain conditions .

Abstract We consider Hardy inequalities in IRn, n ≥ 3, with best constant that involve either distance to the boundary or distance to a surface of co-dimension k < n, and we show that they can still be improved by adding a multiple of a whole range of critical norms that at the extreme case become precisely the critical Sobolev norm. Résumé Nous étudions des inegalités de Hardy dans IRn, n ≥ 3,...

The (bitwise) complement $\overline{x}$ of a binary word $x$ is obtained by changing each $0$ in to $1$ and vice versa. An $\textit{antisquare}$ nonempty the form $x\, \overline{x}$. In this paper, we study infinite words that do not contain arbitrarily large antisquares. For example, show repetition threshold for language containing exactly two distinct antisquares $(5+\sqrt{5})/2$. We also th...

We show that the variational quantum-classical simulation algorithm admits a finite circuit depth scaling collapse when targeting critical point of transverse field Ising chain. The order parameter only collapses on one side transition due to slowdown quantum crossing phase transition. In assess performance and compute correlations in system up 752 qubits, we use techniques from integrability d...