2014 We compute the high frequency elastic distortion of a columnar discotic single crystal submitted to a longitudinal dilation. The ends of the columns are assumed to be clamped and anchored perpendicularly to two infinitely rigid glass plates, on a width L. The local strain close to the plates relaxes to the homogeneous distortion of an unclamped sample on a characteristic length £ ~ (Lm)1/2...

Alternative growth and decay estimates, reminiscent of the classical Phragmén-Lindelöf principle, are derived for a linearised thermoelastic body whose plane cross-sections increase unboundedly with respect to a given direction. The proof uses a modified Poincaré inequality to construct a differential inequality for a weighted linear combination of the cross-sectional mechanical and thermal ene...

Abstract We consider fractional Schrödinger operators with possibly singular potentials and derive certain spatially averaged estimates for its complex-time heat kernel. The main tool is a Phragmén–Lindelöf theorem polynomially bounded functions on the right complex half-plane. interpolation leads to nonoptimal off-diagonal bounds.

The transversely isotropic magnetoelectroelastic solids plane problem in rectangular domain is derived to Hamiltonian system. In symplectic geometry space with the origin variables— displacements, electric potential, and magnetic potential, as well as their duality variables— lengthways stress, electric displacement, and magnetic induction, on the basis of the obtained eigensolutions of zero-ei...

We consider a homogeneous space X = (X, d,m) of dimension ν ≥ 1 and a local regular Dirichlet form in L2 (X,m) . We prove that if a Poincaré inequality of exponent 1 ≤ p < ν holds on every pseudo-ball B (x,R) of X, with local characteristic constant c0 (x) and c1 (r), then a Green’s function estimate from above and below is obtained. A Saint-Venant-like principle is recovered in terms of the En...

Toupin's version of the Saint-Venant principle in linear elasticity is generalized to the case of linear elasticity with mierostructure. That is, it is shown that, for a straight prismatic bar made of an isotropic linear elastic material with rnicrostructure and loaded by a self-equilibrated force system at one end only, the strain energy stored in the portion of the bar which is beyond a dista...

The Phragmén-Lindelöf theorem for Lp-viscosity solutions of fully nonlinear second order elliptic partial differential equations with unbounded coefficients and inhomogeneous terms is established.

We establish two Phragmén–Lindelöf theorems for a fully nonlinear elliptic equation. consider dynamical boundary condition that includes both spatial variable and time derivative terms. As term, we non-linear Neumann-type operator with strict monotonicity in the normal direction of on term. Our first result is an equation epigraph $$\mathbb {R}^n$$ . Because assume good structural condition, wh...