Displaying similar documents to “Ito equation as a geodesic flow on Diff s ( S 1 ) ⨀ C ∞ ( S 1 ) ^ ”

Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case q = 3 d d + 2

Jörg Wolf (2007)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we consider weak solutions 𝐮 : Ω → ℝ d to the equations of stationary motion of a fluid with shear dependent viscosity in a bounded domain Ω ⊂ ℝ d ( d = 2 or d = 3 ). For the critical case q = 3 d d + 2 we prove the higher integrability of ∇ 𝐮 which forms the basis for applying the method of differences in order to get fractional differentiability of ∇ 𝐮 . From this we show the existence of second order weak derivatives of u .

Some estimates for the first eigenvalue of the Sturm-Liouville problem with a weight integral condition

Maria Telnova (2012)

Mathematica Bohemica

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Let λ 1 ( Q ) be the first eigenvalue of the Sturm-Liouville problem y ' ' - Q ( x ) y + λ y = 0 , y ( 0 ) = y ( 1 ) = 0 , 0 < x < 1 . We give some estimates for m α , β , γ = inf Q ∈ T α , β , γ λ 1 ( Q ) and M α , β , γ = sup Q ∈ T α , β , γ λ 1 ( Q ) , where T α , β , γ is the set of real-valued measurable on 0 , 1 x α ( 1 - x ) β -weighted L γ -functions Q with non-negative values such that ∫ 0 1 x α ( 1 - x ) β Q γ ( x ) d x = 1 ( α , β , γ ∈ ℝ , γ ≠ 0 ) .