Displaying similar documents to “Elliptic self-similar stochastic processes.”

Mapping properties of the elliptic maximal function.

M. Burak Erdogan (2003)

Revista Matemática Iberoamericana

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We prove that the elliptic maximal function maps the Sobolev space W4,eta(R2) into L4(R2) for all eta > 1/6. The main ingredients of the proof are an analysis of the intersectiQn properties of elliptic annuli and a combinatorial method of Kolasa and Wolff.

The existence of positive solution to some asymptotically linear elliptic equations in exterior domains.

Gongbao Li, Gao-Feng Zheng (2006)

Revista Matemática Iberoamericana

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In this paper, we are concerned with the asymptotically linear elliptic problem -Δu + λu = f(u), u ∈ H (Ω) in an exterior domain Ω = RO (N ≥ 3) with O a smooth bounded and star-shaped open set, and lim f(t)/t = l, 0 < l < +∞. Using a precise deformation lemma and algebraic topology argument, we prove under our assumptions that the problem possesses at least one positive solution.

Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one.

Alexander V. Sobolev (2006)

Revista Matemática Iberoamericana

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We consider a periodic pseudo-differential operator on the real line, which is a lower-order perturbation of an elliptic operator with a homogeneous symbol and constant coefficients. It is proved that the density of states of such an operator admits a complete asymptotic expansion at large energies. A few first terms of this expansion are found in a closed form.