The improved decay rate for the heat semigroup with local magnetic field in the plane

@article{Krejik2011TheID,
  title={The improved decay rate for the heat semigroup with local magnetic field in the plane},
  author={David Krej{\vc}iř{\'i}k},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2011},
  volume={47},
  pages={207-226}
}
  • David Krejčiřík
  • Published 2011
  • Mathematics, Physics
  • Calculus of Variations and Partial Differential Equations
  • We consider the heat equation in the presence of compactly supported magnetic field in the plane. We show that the magnetic field leads to an improvement of the decay rate of the heat semigroup by a polynomial factor with power proportional to the distance of the total magnetic flux to the discrete set of flux quanta. The proof employs Hardy-type inequalities due to Laptev and Weidl for the two-dimensional magnetic Schrödinger operator and the method of self-similar variables and weighted… CONTINUE READING

    Citations

    Publications citing this paper.
    SHOWING 1-10 OF 12 CITATIONS

    Complex Magnetic Fields: An Improved Hardy-Laptev-Weidl Inequality and Quasi-Self-Adjointness

    VIEW 2 EXCERPTS
    CITES BACKGROUND