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Second order elliptic operators with diffusion coefficients growing as |x|α at infinity
-
Motohiro Sobajima
and
Chiara Spina
Published/Copyright:
January 11, 2015
Abstract
We prove that, for N/(N-2) < p < ∞, α > 2, the operator Lu = (1 + |x|2)α/2Tr(A(x)D2u) = (1 + |x|2)α/2∑i,j=1,...,Naij(x)Diju admits realizations generating analytic semigroups in Lp(ℝN). Moreover, for α < N/p', we provide an explicit description of the domain.
The authors would like to thank Giorgio Metafune for helpful discussions, comments and suggestions on the paper.
Received: 2014-3-28
Revised: 2014-7-18
Published Online: 2015-1-11
Published in Print: 2016-3-1
© 2016 by De Gruyter
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- Ring class invariants over imaginary quadratic fields
- The structure of p-local compact groups of rank 1
- Sampling and interpolation on some nilpotent Lie groups
- Topology of moduli spaces of free group representations in real reductive groups
- Finite symmetries of S4
- Variations of Minkowski's theorem on successive minima
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- Time inhomogeneous generalized Mehler semigroups and skew convolution equations
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- Second order elliptic operators with diffusion coefficients growing as |x|α at infinity
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Keywords for this article
Elliptic operators;
unbounded coefficients;
generation results;
analytic semigroups
Articles in the same Issue
- Frontmatter
- Ring class invariants over imaginary quadratic fields
- The structure of p-local compact groups of rank 1
- Sampling and interpolation on some nilpotent Lie groups
- Topology of moduli spaces of free group representations in real reductive groups
- Finite symmetries of S4
- Variations of Minkowski's theorem on successive minima
- A one-relator group with long lower central series
- On transfinite nilpotence of the Vogel–Levine localization
- Time inhomogeneous generalized Mehler semigroups and skew convolution equations
- Specifying the Auslander–Reiten translation for complexes of modules
- Second order elliptic operators with diffusion coefficients growing as |x|α at infinity
- On the fourth derivative test for exponential sums
