| 1. |
- Avelin, Benny, 1984-, et al.
(författare)
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A comparison principle for the porous medium equation and its consequences
- 2017
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Ingår i: Revista matemática iberoamericana. - 0213-2230 .- 2235-0616. ; 33:2, s. 573-594
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Tidskriftsartikel (refereegranskat)abstract
- We prove a comparison principle for the porous medium equation in more general open sets in Rn+1 than space-time cylinders. We apply this result in two related contexts: we establish a connection between a potential theoretic notion of the obstacle problem and a notion based on a variational inequality. We also prove the basic properties of the PME capacity, in particular that there exists a capacitary extremal which gives the capacity for compact sets.
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| 2. |
- Bakas, Odysseas, et al.
(författare)
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A class of multiparameter oscillatory singular integral operators : endpoint Hardy space bounds
- 2020
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Ingår i: Revista matemática iberoamericana. - 0213-2230 .- 2235-0616. ; 36:2, s. 611-639
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Tidskriftsartikel (refereegranskat)abstract
- We establish endpoint bounds on a Hardy space H1 for a natural class of multiparameter singular integral operators which do not decay away from the support of rectangular atoms. Hence the usual argument via a Journé-type covering lemma to deduce bounds on product H1 is not valid.We consider the class of multiparameter oscillatory singular integral operators given by convolution with the classical multiple Hilbert transform kernel modulated by a general polynomial oscillation. Various characterisations are known which give L2 (or more generally Lp, 1<p<∞) bounds. Here we initiate an investigation of endpoint bounds on the rectangular Hardy space H1 in two dimensions; we give a characterisation when bounds hold which are uniform over a given subspace of polynomials and somewhat surprisingly, we discover that the Hardy space and Lp theories for these operators are very different.
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| 3. |
- Balkanova, Olga, 1988, et al.
(författare)
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Convolution formula for the sums of generalized Dirichlet L-functions
- 2019
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Ingår i: Revista Matematica Iberoamericana. - : European Mathematical Society - EMS - Publishing House GmbH. - 0213-2230 .- 2235-0616. ; 35:7, s. 1973-1995
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Tidskriftsartikel (refereegranskat)abstract
- Using the Kuznetsov trace formula, we prove a spectral decomposition for the sums of generalized Dirichlet L-functions. Among applications are an explicit formula relating norms of prime geodesics to moments of symmetric square L-functions and an asymptotic expansion for the average of central values of generalized Dirichlet L-functions.
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| 4. |
- Bandyopadhyay, Antar, 1973, et al.
(författare)
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On the Cluster Size Distribution for Percolation on Some General Graphs
- 2010
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Ingår i: Revista Matematica Iberoamericana. - 0213-2230 .- 2235-0616. ; 26, s. 529-550
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Tidskriftsartikel (refereegranskat)abstract
- We show that for any Cayley graph, the probability (at any p) that the cluster of the origin has size n decays at a well-defined exponential rate (possibly 0). For general graphs, we relate this rate being positive in the supercritical regime with the amenability/nonamenability of the underlying graph.
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| 5. |
- Baroni, Paolo, et al.
(författare)
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Calderon-Zygmund estimates for parabolic p(x, t)-Laplacian systems
- 2014
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Ingår i: Revista matemática iberoamericana. - 0213-2230 .- 2235-0616. ; 30:4, s. 1355-1386
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Tidskriftsartikel (refereegranskat)abstract
- We prove local Calderon-Zygmund estimates for weak solutions of the evolutionary p(x, t)-Laplacian system partial derivative(t)u - div (a(x, t)vertical bar Du vertical bar(p(x,t)-2)Du) = div (vertical bar F vertical bar F-p(x,F-t)-2 under the classical hypothesis of logarithmic continuity for the variable exponent p(x, t). More precisely, we show that the spatial gradient Du of the solution is as integrable as the right-hand side F, i.e., vertical bar F vertical bar(p(.)) is an element of L-loc(q) double right arrow vertical bar Du vertical bar(p(.)) is an element of L-loc(q) for any q > 1, together with quantitative estimates. Thereby we allow the presence of eventually discontinuous coefficients a(x, t), requiring only a VMO condition with respect to the spatial variable x.
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| 6. |
- Björn, Anders, et al.
(författare)
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Obstacle and Dirichlet problems on arbitrary nonopen sets in metric spaces, and fine topology
- 2015
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Ingår i: Revista matemática iberoamericana. - : Universidad Autonoma de Madrid, Departamento de Matematicas / European Mathematical Society. - 0213-2230 .- 2235-0616. ; 31:1, s. 161-214
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Tidskriftsartikel (refereegranskat)abstract
- We study the double obstacle problem for p-harmonic functions on arbitrary bounded nonopen sets E in quite general metric spaces. The Dirichlet and single obstacle problems are included as special cases. We obtain the Adams criterion for the solubility of the single obstacle problem and establish connections with fine potential theory. We also study when the minimal p-weak upper gradient of a function remains minimal when restricted to a nonopen subset. Many of the results are new even for open E (apart from those which are trivial in this case) and also on R-n.
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| 7. |
- Björn, Anders, et al.
(författare)
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Removable sets for Newtonian Sobolev spaces and a characterization of p-path almost open sets
- 2023
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Ingår i: Revista matemática iberoamericana. - : EUROPEAN MATHEMATICAL SOC-EMS. - 0213-2230 .- 2235-0616. ; 39:3, s. 1143-1180
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Tidskriftsartikel (refereegranskat)abstract
- We study removable sets for Newtonian Sobolev functions in metric measure spaces satisfying the usual (local) assumptions of a doubling measure and a Poincare inequality. In particular, when restricted to Euclidean spaces, a closed set E c Rn with zero Lebesgue measure is shown to be removable for W1;p.Rn \ E/ if and only if Rn \ E supports a p-Poincare inequality as a metric space. When p > 1, this recovers Koskelas result (Ark. Mat. 37 (1999), 291-304), but for p = 1, as well as for metric spaces, it seems to be new. We also obtain the corresponding characterization for the Dirichlet spaces L1;p. To be able to include p = 1, we first study extensions of Newtonian Sobolev functions in the case p = 1 from a noncom-plete space X to its completion Xy. In these results, p-path almost open sets play an important role, and we provide a characterization of them by means of p-path open, p-quasiopen and p-finely open sets. We also show that there are nonmeasurable p -path almost open subsets of Rn, n > 2, provided that the continuum hypothesis is assumed to be true. Furthermore, we extend earlier results about measurability of functions with Lp-integrable upper gradients, about p-quasiopen, p-path open and p-finely open sets, and about Lebesgue points for N1;1-functions, to spaces that only satisfy local assumptions.
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| 8. |
- Björn, Anders, et al.
(författare)
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The Dirichlet problem for p-harmonic functions with respect to arbitrary compactifications
- 2018
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Ingår i: Revista matemática iberoamericana. - : EUROPEAN MATHEMATICAL SOC. - 0213-2230 .- 2235-0616. ; 34:3, s. 1323-1360
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Tidskriftsartikel (refereegranskat)abstract
- We study the Dirichlet problem for p-harmonic functions on metric spaces with respect to arbitrary compactifications. A particular focus is on the Perron method, and as a new approach to the invariance problem we introduce Sobolev-Perron solutions. We obtain various resolutivity and invariance results, and also show that most functions that have earlier been proved to be resolutive are in fact Sobolev-resolutive. We also introduce (Sobolev)-Wiener solutions and harmonizability in this nonlinear context, and study their connections to (Sobolev)-Perron solutions, partly using Q-compactifications.
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| 9. |
- Damian, Wendolin, et al.
(författare)
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New bounds for bilinear Calderon-Zygmund operators and applications
- 2018
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Ingår i: Revista Matematica Iberoamericana. - : European Mathematical Society - EMS - Publishing House GmbH. - 0213-2230 .- 2235-0616. ; 34:3, s. 1177-1210
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Tidskriftsartikel (refereegranskat)abstract
- In this work we extend Lacey's domination theorem to prove the pointwise control of bilinear Calderon-Zygmund operators with Dini-continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a recent work of Hytonen, Roncal and Tapiola. We also derive new mixed weighted estimates for a general class of bilinear dyadic positive operators using multiple A(infinity), constants inspired in the Fujii-Wilson and Hruscev classical constants. These estimates have many new applications including mixed bounds for multilinear Calderon-Zygmund operators and their commutators with BMO functions, square functions and multilinear Fourier multipliers.
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| 10. |
- Dooley, Anthony H., et al.
(författare)
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On Lp improving measures
- 2016
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Ingår i: Revista matemática iberoamericana. - 0213-2230 .- 2235-0616. ; 32, s. 1211-1226
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Tidskriftsartikel (refereegranskat)abstract
- © European Mathematical Society.We give criteria for establishing that a measure is Lp-improving. Many Riesz product measures and Cantor measures satisfy this criteria, as well as certain Markov measures.
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