| 1. |
- Benedicks, Michael, et al.
(författare)
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Random perturbations and statistical properties of Henon-like maps
- 2006
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Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 23:5, s. 713-752
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Tidskriftsartikel (refereegranskat)abstract
- For a large class of non-uniformly hyperbolic diffeomorphisms, we prove stochastic stability under small random noise: the unique stationary probability measure of the Markov chain converges to the Sinai-Ruelle-Bowen measure of the unperturbed attractor when the noise level tends to zero.
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| 2. |
- Bona, J L, et al.
(författare)
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Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation
- 2005
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Ingår i: Annales de L'Institut Henri Poincaré. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449. ; 22:6, s. 783-797
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Tidskriftsartikel (refereegranskat)abstract
- The generalized Korteweg-de Vries equation has the property that solutions with initial data that are analytic in a strip in the complex plane continue to be analytic in a strip as time progresses. Established here are algebraic lower bounds on the possible rate of decrease in time of the uniform radius of spatial analyticity for these equations. Previously known results featured exponentially decreasing bounds.
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| 3. |
- Lindgren, Erik, et al.
(författare)
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On the two-phase membrane problem with coefficients below the Lipschitz threshold
- 2009
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Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 26:6, s. 2359-2372
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Tidskriftsartikel (refereegranskat)abstract
- We study the regularity of the two-phase membrane problem, with coefficients below the Lipschitz threshold. For the Lipschitz coefficient case one can apply a monotonicity formula to prove the C-1,C-1-regularity of the solution and that the free boundary is, near the so-called branching points, the union of two C-1-graphs. In our case, the same monotonicity formula does not apply in the same way. In the absence of a monotonicity formula, we use a specific scaling argument combined with the classification of certain global solutions to obtain C-1,C-1-estimates. Then we exploit some stability properties with respect to the coefficients to prove that the free boundary is the union of two Reifenberg vanishing sets near so-called branching points.
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| 4. |
- Pinchover, Yehuda, et al.
(författare)
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A Liouville-type theorem for the p-Laplacian with potential term
- 2008
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Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 25:2, s. 357-368
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a singular p-Laplacian problem with a potential term, such that a nonzero subsolution of another such problem is also a ground state. Unlike in the linear case (p = 2), this condition involves comparison of both the functions and of their gradients.
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