We present a quasi-local version of the stability positive mass theorem. work with Brown–York as it possesses positivity and rigidity properties, therefore this statement can be studied. Specifically, we ask if boundary some compact manifold is close to zero, must Euclidean domain in sense? Here consider class <mml:math xmlns:mml="http://www.w3.org/19...

Contents 1 Introduction 2 2 The Dirichlet problem and the boundary trace 7 2. Abstract We study the boundary value problem with measures for (E1) −∆u + g(|∇u|) = 0 in a bounded domain Ω in R N , satisfying (E2) u = µ on ∂Ω and prove that if g ∈ L 1 (1, ∞; t −(2N +1)/N dt) is nondecreasing (E1)-(E2) can be solved with any positive bounded measure. When g(r) ≥ r q with q > 1 we prove that any pos...

Here D ⊂ R is a bounded domain with Lipschitz boundary ΓD, E is the electric field, H is the magnetic field, x̂ = x/|x|, and n is the unit outer normal to ΓD. The applied current J and the initial conditions E0,H0 are assumed to be supported in the circle BR = {x ∈ R : |x| < R} for some R > 0. The electric permittivity ε and magnetic permeability μ are assumed to be positive constants. We remark...

We report on very recent work on the stabilization of the steady-state solutions to Navier-Stokes equations on an open bounded domain R C Rd, d = 2,3, by either interior, or else boundary control. More precisely, as to the interior case, we obtain that the steadystate solutions to Navier-Stokes equations on R C Rd, d = 2,3, with no-slip boundary conditions, are locally exponentially stabilizabl...

We study boundary and finite-size effects in the Abelian sandpile model due to Bak, Tang and Wiesenfeld. In the case of half-plane geometry, the probability iPj (r ) of a unit height at the boundary, and at a distance r inside the sample is found for open and closed boundary conditions. The leading asymptotic form of the correlation functions for the unit heights, tPj, (r), in the strip and hal...

Convection in an isolated planet is characterized by narrow downwellings and broad updrafts--consequences of Archimedes' principle, the cooling required by the second law of thermodynamics, and the effect of compression on material properties. A mature cooling planet with a conductive low-viscosity core develops a thick insulating surface boundary layer with a thermal maximum, a subadiabatic in...

Abstract We describe some sufficient conditions, under which smooth and compactly supported functions are or not dense in the fractional Sobolev space $$W^{s,p}(\Omega )$$ W s , p ( Ω <mml:mo...

Abstract. We calculate the boundary correlation function of fixed-to-free boundary condition changing operators in the square-lattice Ising model. The correlation function is expressed in four different ways using 2×2 block Toeplitz determinants. We show that these can be transformed into a scalar Toeplitz determinant when the size of the matrix is even. To know the asymptotic behavior of the c...

biostratigraphy of bahram formation succession, with 359.8 meter thickness, in the sardar section (north of kerman, central iran) is done in this study. bahram formation is mostly composed of limestones (with a lesser amount of sandstones), and conformably overlies the top sandstone beds of the padeha formation. but, the upper boundary with the hutk formation (late tounaisian) is disconformable...