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Sökning: L773:1435 9855

  • Resultat 1-10 av 25
  • [1]23Nästa
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1.
  • Ekholm, Tobias (författare)
  • Rational symplectic field theory over Z_2 for exact Lagrangian cobordisms
  • 2008
  • Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 10:3, s. 641-704
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>We construct a version of rational symplectic field theory for pairs (X, L), where X is an exact symplectic manifold, where L ⊂ X is an exact Lagrangian submanifold with components subdivided into k subsets, and where both X and L have cylindrical ends. The theory associates to (X, L) a Z-graded chain complex of vector spaces over Z_2 , filtered with k filtration levels. The corresponding k -level spectral sequence is invariant under deformations of (X, L) and has the following property: if (X, L) is obtained by joining a negative end of a pair (X, L) to a positive end of a pair (X, L), then there are natural morphisms from the spectral sequences of (X, L) and of (X ,L) to the spectral sequence of (X, L). As an application, we show that if \Lambda ⊂ Y is a Legendrian submanifold of a contact manifold then the spectral sequences associated to (Y × R, \Lambda_s × R), where Y × R is the symplectization of Y and where \Lambda_s ⊂ Y is the Legendrian submanifold consisting of s parallel copies of \Lambda subdivided into k subsets, give Legendrian isotopy invariants of \Lambda.</p>
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2.
  • Andersen, Henning Haahr, et al. (författare)
  • Category O for quantum groups
  • 2015
  • Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 17:2, s. 405-431
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>We study the BGG-categories O-q associated to quantum groups. We prove that many properties of the ordinary BGG-category O for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when q is a complex root of unity. Here we prove a tensor decomposition for simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for O and for finite-dimensional U-q-modules we are able to determine all irreducible characters as well as the characters of all indecomposable tilting modules in O-q. As a consequence, we also recover the known result that the generic quantum case behaves like the classical category O.</p>
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3.
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4.
  • Auscher, Pascal, et al. (författare)
  • L2 well-posedness of boundary value problems and the Kato square root problem for parabolic systems with measurable coefficients
  • 2016
  • Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863.
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>We introduce a first order strategy to study boundary value problems of parabolic systems with second order elliptic part in the upper half-space. This involves a parabolic Dirac operator at the boundary. We allow for measurable time dependence and some transversal dependence in the coefficients. We obtain layer potential representations for solutions in some classes and prove new well-posedness and perturbation results. As a byproduct, we prove for the first time a Kato estimate for the square root of parabolic operators with time dependent coefficients. This considerably extends prior results obtained by one of us under time and transversal independence. A major difficulty compared to a similar treatment of elliptic equations is the presence of non-local fractional derivatives in time.</p>
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5.
  • Avelin, Benny, 1984-, et al. (författare)
  • Boundary Estimates for Certain Degenerate and Singular Parabolic Equations
  • 2016
  • Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 18:2, s. 381-424
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic p-Laplace equation. Assuming that such solutions continuously vanish on some distinguished part of the lateral part S-T of a Lipschitz cylinder, we prove Carleson-type estimates, and deduce some consequences under additional assumptions on the equation or the domain. We then prove analogous estimates for non-negative solutions to a class of degenerate/singular parabolic equations of porous medium type.</p>
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6.
  • Canto-Martín, Francisco, et al. (författare)
  • Perron-Frobenius operators and the Klein-Gordon equation
  • 2014
  • Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 16:1, s. 31-66
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>For a smooth curve Gamma and a set Lambda in the plane R-2, let AC(Gamma; Lambda) be the space of finite Borel measures in the plane supported on Gamma, absolutely continuous with respect to arc length and whose Fourier transform vanishes on Lambda. Following [12], we say that (Gamma, Lambda) is a Heisenberg uniqueness pair if AC(Gamma; Lambda) = {0}. In the context of a hyperbola Gamma, the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets Gamma of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the issue of finding the dimension of AC(Gamma; Lambda) when it is nonzero. We will fix the curve Gamma to be the hyperbola x(1)x(2) = 1, and the set Lambda = Lambda(alpha,beta) to be the lattice-cross Lambda(alpha,beta) = (alpha Zeta x {0}) boolean OR ({0} x beta Z), where alpha, beta are positive reals. We will also consider Gamma(+), the branch of x(1)x(2) = 1 where x(1) &gt; 0. In [12], it is shown that AC(Gamma; Lambda(alpha,beta)) = {0} if and only if alpha beta &lt;= 1. Here, we show that for alpha beta &gt; 1, we get a rather drastic "phase transition": AC(Gamma; Lambda(alpha,beta)) is infinite-dimensional whenever alpha beta &gt; 1. It is shown in [13] that AC(Gamma(+); Lambda(alpha,beta)) = {0} if and only if alpha beta &lt; 4. Moreover, at the edge alpha beta = 4, the behavior is more exotic: the space AC(Gamma(+); Lambda(alpha,beta)) is one-dimensional. Here, we show that the dimension of AC(Gamma(+); Lambda(alpha,beta)) is infinite whenever alpha beta &gt; 4. Dynamical systems, and more specifically Perron-Frobenius operators, play a prominent role in the presentation.</p>
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7.
  • Cianchi, Andrea, et al. (författare)
  • Gradient regularity via rearrangements for p-Laplacian type elliptic boundary value problems
  • 2014
  • Ingår i: Journal of the European Mathematical Society (Print). - European Mathematical Society. - 1435-9855 .- 1435-9863. ; 16:3, s. 571-595
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>A sharp estimate for the decreasing rearrangement of the length of the gradient of solutions to a class of nonlinear Dirichlet and Neumann elliptic boundary value problems is established under weak regularity assumptions on the domain. As a consequence, the problem of gradient bounds in norms depending on global integrability properties is reduced to one-dimensional Hardy-type inequalities. Applications to gradient estimates in Lebesgue, Lorentz, Zygmund, and Orlicz spaces are presented.</p>
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8.
  • Dolbeault, Jean, et al. (författare)
  • Lieb-Thirring inequalities with improved constants
  • 2008
  • Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 10:4, s. 1121-1126
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one dimension. This allows us to improve on the known estimates of best constants in Lieb-Thirring inequalities for the sum of the negative eigenvalues for multidimensional Schrodinger operators.</p>
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9.
  • Ekholm, Tobias, 1970-, et al. (författare)
  • Legendrian knots and exact Lagrangian cobordisms
  • 2016
  • Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 18:11, s. 2627-2689
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>We introduce constructions of exact Lagrangian cobordisms with cylindrical Legendrian ends and study their invariants which arise from Symplectic Field Theory. A pair (X, L) consisting of an exact symplectic manifold X and an exact Lagrangian cobordism L subset of X which agrees with cylinders over Legendrian links Lambda(+) and Lambda (-) at the positive and negative ends induces a differential graded algebra (DGA) map from the Legendrian contact homology DGA of Lambda(+) to that of Lambda (-) .We give a gradient flow tree description of the DGA maps for certain pairs (X, L), which in turn yields a purely combinatorial description of the cobordism map for elementary cobordisms, i.e., cobordisms that correspond to certain local modifications of Legendrian knots. As an application, we find exact Lagrangian surfaces that fill a fixed Legendrian link and are not isotopic through exact Lagrangian surfaces.</p>
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10.
  • Ekholm, Tomas, et al. (författare)
  • Lieb-Thirring inequalities on the half-line with critical exponent
  • 2008
  • Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 10:3, s. 739-755
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>We consider the operator -d(2)/dr(2) - V in L-2(R+) with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound for any alpha is an element of [0, 1) and gamma &gt;= (1 - alpha)/2. This includes a Lieb-Thirring inequality in the critical endpoint case.</p>
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