Wyniki wyszukiwania

1

Estimates of Green functions and their applications for parabolic operators with singular potentials

100%

Riahi L.

Colloquium Mathematicum

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2003

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tom 95

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nr 2

267-283

EN

We prove global pointwise estimates for the Green function of a parabolic operator with potential in the parabolic Kato class on a $C^{1,1}$ cylindrical domain Ω. We apply these estimates to obtain a new and shorter proof of the Harnack inequality [16], and to study the boundary behavior of nonnegative solutions.

2

A 3G-Theorem for Jordan Domains in ℝ²

100%

Riahi L.

Colloquium Mathematicum

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2004

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tom 101

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nr 1

1-7

EN

We prove a new 3G-Theorem for the Laplace Green function G on an arbitrary Jordan domain D in ℝ². This theorem extends the recent one proved on a Dini-smooth Jordan domain.

3

On the equivalence of Green functions for general Schrödinger operators on a half-space

63%

Ifra A., Riahi L.

Annales Polonici Mathematici

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2004

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tom 83

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nr 1

65-76

EN

We consider the general Schrödinger operator $L = div(A(x)∇_x) - μ$ on a half-space in ℝⁿ, n ≥ 3. We prove that the L-Green function G exists and is comparable to the Laplace-Green function $G_{Δ}$ provided that μ is in some class of signed Radon measures. The result extends the one proved on the half-plane in [9] and covers the case of Schrödinger operators with potentials in the Kato class at infinity $Kₙ^{∞}$ considered by Zhao and Pinchover. As an application we study the cone $𝓒_L(ℝⁿ₊)$ of all positive L-solutions continuously vanishing on the boundary {xₙ = 0}.

Ograniczanie wyników

2 Colloquium Mathematicum

1 Annales Polonici Mathematici

3 Riahi L.

1 Ifra A.

2 2004

1 2003

Estimates of Green functions and their applications for parabolic operators with singular potentials

A 3G-Theorem for Jordan Domains in ℝ²

On the equivalence of Green functions for general Schrödinger operators on a half-space