Analysis of Heat Equations on Domains

By El-Maati Ouhabaz. 2004

843 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/463115156ab36f72f285710e268caf269570a5b7

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Citations in the corpus

Resolvent at low energy and Riesz transform for Schrödinger operators on asymptotically conic manifolds. I. (2007, background): “Ouhabaz [19]), which means again a quite strong stability for low range of p.”
A MAXIMAL FUNCTION CHARACTERIZATION FOR HARDY SPACES ASSOCIATED TO NONNEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES (2015, unknown): “18, [21].”
Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2012, background): “One can see that by combining the results in [9, 45] and [13], this estimate and the doubling condition (1.”
Restriction estimates, sharp spectral multipliers and endpoint estimates for Bochner-Riesz means (2012, unknown): “We refer the reade r to [2, 12, 14, 15, 16, 17, 21, 23, 24, 25, 26, 27, 28, 30, 32, 34, 44, 47, 48, 50, 53, 54, 56, 58, 59, 61, 63, 64] and the references therein.”
Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem (2010, result): “positive and contractive, then, according to the result by Liskevich and Perelmuter [26] (see also [29], Theorem 3.”
Orlicz-Hardy spaces associated with operators (2009, background): “g may depend on k but it always satisfies (2.2); see Theorem 6.17 of [ 19 ] and [20].”
Riesz Transforms of Schrödinger Operators on Manifolds (2012, unknown): “Let us also mention the following works of Auscher [2], Blunck and Kunstmann [9], Sikora [27] and Ouhabaz [25] (Chapter 7) dealing with Riesz transforms of elliptic differential operators.”
The Dirichlet-to-Neumann operator on rough domains (2010, unknown): “But this implies that S is ultracontractive by [20], Lemma 6.”
Endpoint estimates for Riesz transforms of magnetic Schrödinger operators (2006, background): “5) The latter equality follows from the fact that for any symmetric form Q associated with an operator A, one has D(Q)=D(A1/2) and Q(u, v)=(Au,Av) (see, for example, Chapter VI of [15] or Chapter 7 of [17]).”
Maximal Lp-regularity for parabolic and elliptic equations on the line (2006, background): “which allows Gaussian upper bounds (see [ Ouh04 ], [AtE97], [Are04]).”
Maximal function characterizations for Hardy spaces on spaces of homogeneous type with finite measure and applications (2018, unknown): “) gives |I2| . exp − r2 c′t ˆ B(x0,2r)\B(x0,3r/2) 1 tn/2 exp − |x−y|2 2ct dx. √ t r e− r2 c′t . For the term I1 we ﬁrst note that qt(x,y) = tLD[pt(·,y)](x) and pt(·,y) ∈ D(LD). See for example [30]. Hence, from (33) and (30), coupled with the support property of ∇ψ, we have (35) |I1| = t ˆ Ω A∇xp”
Weighted norm inequalities, Gaussian bounds and sharp spectral multipliers (2010, background): “Such estimates are typical for elliptic or sub-elliptic differential operators of order m (see for instance, [9,14,27,28] and [39]).”
Maximal parabolic regularity for divergence operators including mixed boundary conditions (2008, unknown): “R + and for all ε>0 there exist constants c,b>0, such that 0 ≤ Kt(x,y) ≤ c td/2 e−b |x−y|2 t eεt, t>0,a.a.x,y ∈ Ω. (3.11) This follows from the following simpliﬁed version of Theorem 6.10 in [75] (see also [7]). Proposition 3.10 (Ouhabaz). Assume that −∇·ω∇, with ω∈ L∞(Ω;L(Rd)) uniformly el”
Thomas Bayes’ walk on manifolds (2012, methodology): “For this section, we follow standard expositions for heat kernel theory: for more details see [22], [26], [15].”