This paper is devoted to several existence results for a generalized version of the Yamabe problem. First, we prove remaining global cases range powers $\gamma\in (0,1)$ problem introduced by Gonzalez and Qing. Second, building on new approach Case Chang this problem, that solvable in Poincar\'{e}-Einstein case (1,\min\{2,n/2\})$ provided associated fractional GJMS operator satisfies strong max...

We introduce a many-body topological invariant, called the disorder parameter (TDP), to characterize gapped quantum phases with global internal symmetry in $2+1$ dimensions. TDP is defined as constant correction that appears ground-state expectation value of partial transformation applied connected spatial region $M$, absolute which scales generically $exp(\ensuremath{-}\ensuremath{\alpha}l+\en...

Abstract We prove that under the log-Hölder continuity condition of variable exponent $$p(\cdot )$$ p ( · ) , a new type maximal operators, $$U_{\gamma ,s}$$ U γ , s<...

We establish the optimal $C_{H}^{1,1}$ interior regularity of solutions to \[ \Delta_{H}u=f\chi_{\{u\ne0\}}, \] where $\Delta_{H}$ denotes sub-Laplacian operator in a stratified group. assume weakest condition on $f$, namely $f*\Gamma$ is $C_{H}^{1,1}$, $\Gamma$ fundamental solution $\Delta_{H}$. The understood sense Folland and Stein. In classical Euclidean setting, first seeds above problem a...

We study the spectrum $\{\lambda_j(m)\}_{j=1}^{\infty}$ of a timelike Killing vector field $Z$ acting as differential operator $D_Z$ on Hilbert space solutions massive Klein-Gordon equation $(\Box_g + m^2) u = 0$ globally hyperbolic stationary spacetime $(M, g)$ with compact Cauchy hypersurface. The inverse mass $m^{-1}$ is formally like Planck constant in Schr\"odinger equation, and we give We...

Let Ω $\Omega$ be a bounded domain of R d $\mathbb {R}^d$ with Lipschitz boundary Γ $\Gamma$ . We define the Dirichlet-to-Neumann operator N $\mathcal {N}$ on L 2 ( ) $L_2(\Gamma )$ associated second-order elliptic A = − ∑ k , j 1 ∂ c l + b · 0 $A -\sum _{k,j=1}^d \partial _k (c_{kl} \, _l) \sum _{k=1}^d (b_k - _k(c_k \cdot )) a_0$ prove criterion for invariance closed convex set under action s...

Background: Heat stress in the steel industry is considered as a serious threat to the health and safety of workers. A wide spectrum of complications and diseases from mild disorders such as burning sensation to fatal conditions such as thermal shock may occur due to uncontrolled thermal stress. In this study, heat stress assessment was performed according to the wet-bulb globe temperature (WBG...