منابع مشابه
Non-linear Rough Heat Equation
This article is devoted to define and solve an evolution equation of the form dyt = ∆yt dt + dXt(yt), where ∆ stands for the Laplace operator on a space of the form L(R), and X is a finite dimensional noisy nonlinearity whose typical form is given by Xt(φ) = ∑N i=1 x i tfi(φ), where each x = (x , . . . , x) is a γ-Hölder function generating a rough path and each fi is a smooth enough function d...
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We study the existence of non–trivial solutions to the Yamabe equation: −∆u+ a(x) = μu|u| 4 n−2 μ > 0, x ∈ Ω ⊂ R with n ≥ 4, u(x) = 0 on ∂Ω under weak regularity assumptions on the potential a(x). More precisely in dimension n ≥ 5 we assume that: (1) a(x) belongs to the Lorentz space L n 2 (Ω) for some 1 ≤ d < ∞, (2) a(x) ≤ M < ∞ a.e. x ∈ Ω, (3) the set {x ∈ Ω|a(x) < 0} has positive measure, (4...
متن کاملNon-linear rough heat equations
This article is devoted to define and solve an evolution equation of the form dyt = yt dt + d Xt (yt ), where stands for the Laplace operator on a space of the form L p(Rn), and X is a finite dimensional noisy nonlinearity whose typical form is given by Xt (φ) = ∑N i=1 xi t fi (φ), where each x = (x (1), . . . , x (N ) is a γ -Hölder function generating a rough path and each fi is a smooth enou...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2015
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-015-0650-8