Displaying similar documents to “The Neumann problem for some degenerate elliptic equations”

Pointwise estimates of nonnegative subsolutions of quasilinear elliptic equations at irregular boundary points

Jan Malý (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let u be a weak solution of a quasilinear elliptic equation of the growth p with a measure right hand term μ . We estimate u ( z ) at an interior point z of the domain Ω , or an irregular boundary point z ∈ ∂ Ω , in terms of a norm of u , a nonlinear potential of μ and the Wiener integral of 𝐑 n ∖ Ω . This quantifies the result on necessity of the Wiener criterion.

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 ) .