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Displaying similar documents to “On L p -estimates for the time dependent Schrödinger operator on L 2 .”

Modulation space estimates for Schrödinger type equations with time-dependent potentials

Wei Wei (2014)

Czechoslovak Mathematical Journal

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We give a new representation of solutions to a class of time-dependent Schrödinger type equations via the short-time Fourier transform and the method of characteristics. Moreover, we also establish some novel estimates for oscillatory integrals which are associated with the fractional power of negative Laplacian ( - Δ ) κ / 2 with 1 ≤ κ ≤ 2 . Consequently the classical Hamiltonian corresponding to the previous Schrödinger type equations is studied. As applications, a series of new boundedness results for...

A note on the Cahn-Hilliard equation in H 1 ( ℝ N ) involving critical exponent

Jan W. Cholewa, Aníbal Rodríguez-Bernal (2014)

Mathematica Bohemica

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We consider the Cahn-Hilliard equation in H 1 ( ℝ N ) with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as | u | → ∞ and logistic type nonlinearities. In both situations we prove the H 2 ( ℝ N ) -bound on the solutions and show that the individual solutions are suitably attracted by the set of equilibria. This complements the results in the literature; see J. W. Cholewa, A. Rodriguez-Bernal (2012).