117,791 research outputs found
The role of an integration identity in the analysis of the Cauchy-Leray transform
No full textThe purpose of this paper is to complement the results by Lanzani and Stein (2017) by showing the dense definability of the Cauchy-Leray transform for the domains that give the counterexamples of Lanzani and Stein (2017), where Lp-boundedness is shown to fail when either the “near” C2boundary regularity, or the strong C-linear convexity assumption is dropped
The mixed problem in L p for some two-dimensional Lipschitz domains
No full textWe consider the mixed problem, {Δ u = 0 in Ω ∂u = f N on N u = fD on D in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. We suppose the Dirichlet data, f D , has one derivative in L p (D) of the boundary and the Neumann data, f N , is in L p (N). We find a p 0 > 1 so that for p in an interval (1, p 0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L p . © 2008 Springer-Verlag
Szegö projections for hardy spaces of monogenic functions and applications
No full textWe introduce Szegö projections for Hardy spaces of monogenic functions defined on a bounded domain Ω in □n. We use such projections to obtain explicit orthogonal decompositions for L 2 (bΩ). As an application, we obtain an explicit representation of the solution of the Dirichlet problem for balls and half spaces with L 2, Clifford algebra-valued, boundary datum. © 2002 Hindawi Publishing Corporation. All rights reserved
Regularity of a ∂ ̄ -Solution Operator for Strongly C -Linearly Convex Domains with Minimal Smoothness
No full textWe prove regularity of solutions of the ∂ ̄ -problem in the Hölder–Zygmund spaces of bounded, strongly C-linearly convex domains of class C1 , 1. The proofs rely on a new analytic characterization of said domains which is of independent interest, and on techniques that were recently developed by the first-named author to prove estimates for the ∂ ̄ -problem on strongly pseudoconvex domains of class C2
The Poisson's problem for the Laplacian with Robin boundary condition in non-smooth domains
No full textGiven a bounded Lipschitz domain Ω ⊂ Rn n ≥ 3, we prove that the Poisson's problem for the Laplacian with right-hand side in L-tp(Ω), Robin-type boundary datum in the Besov space Bp1-1/p-t,p(∂Ω) and non-negative, non-everywhere vanishing Robin coefficient b ∈ L n-1(∂ω), is uniquely solvable in the class L 2-tp(Omega;) for (t, 1/p) ∈ νε, where νε (ε ≥ 0) is an open (Ω,b)-dependent plane region and ν0 is to be interpreted ad the common (optimal) solvability region for all Lipschitz domains. We prove a similar regularity result for the Poisson's problem for the 3-dimensional Lamé System with traction-type Robin boundary condition. All solutions are expressed as boundary layer potentials
Szegö and Bergman projections on non-smooth planar domains
No full textWe establish L p regularity for the Szegö and Bergman projections associated to a simply connected planar domain in any of the following classes: vanishing chord arc; Lipschitz; Ahlfors-regular; or local graph (for the Szegö projection to be well defined, the local graph curve must be rectifiable). As applications, we obtain L p regularity for the Riesz transforms, as well as Sobolev space regularity for the non-homogeneous Dirichlet problem associated to any of the domains above and, more generally, to an arbitrary proper simply connected domain in the plane. © 2004 Mathematica Josephina, Inc
Szego projection versus potential theory for non-smooth planar domains
No full textWe show that the Kerzman-Stein operator associated to a bounded planar domain Ω with C1-boundary is compact in L2(bΩ). We establish the Kerzman-Stein equation for the Szego projection associated to a bounded planar domain with Lipschitz boundary. As an application, we extend to the Lipschitz setting a theorem of S. Bell for representing the solution of the classical Dirichlet problem on a simply connected bounded domain in the complex plane
Nuovi parchi agro-sociali: infrastrutture di cittadinanza nei territori periurbani
No full textsaggio sul ruolo dei parchi perturbati multifunzionali in cui la dimensione sociale (intesa come contributo alla conduzione da parte di associazioni, enti e gruppi di cittadini la cui finalità è l'inclusione sociale e la promozione del lavoro) è funzionale alla riorganizzazione di territori caratterizzati da fragilità ambientali, economiche e sociali
L' interpretazione dei contesti locali negli anni cinquanta : contributi all'indagine e alla progettazione territoriale dal dopoguerra ai primi anni sessanta
No full textSymmetrization of a Cauchy-like kernel on curves
No full textGiven a curve Γ⊂C with specified regularity, we investigate boundedness and positivity for a certain three-point symmetrization of a Cauchy-like kernel KΓ whose definition is dictated by the geometry and complex function theory of the domains bounded by Γ. Our results show that S[ReKΓ] and S[ImKΓ] (namely, the symmetrizations of the real and imaginary parts of KΓ) behave very differently from their counterparts for the Cauchy kernel previously studied in the literature. For instance, the quantities S[ReKΓ](z) and S[ImKΓ](z) can behave like [Formula presented] and [Formula presented], where z is any three-tuple of points in Γ and c(z) is the Menger curvature of z. For the original Cauchy kernel, an iconic result of M. Melnikov gives that the symmetrized forms of the real and imaginary parts are each equal to [Formula presented] for all three-tuples in C
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