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S. Fornaro, L. Lorenzi (2007)
Generation results for elliptic operators with unbounded diffusion coefficients in $L^p$- and $C_b$-spacesDiscrete and Continuous Dynamical Systems, 18
P. Bassanini, A. Elcrat (1997)
Elliptic Partial Differential Equations of Second Order
M. Dothan (1978)
On the term structure of interest ratesJ. Financial Economics, 7
(1978)
Interpolation Theory
(1983)
Semigroups of linear operators and applications to partial differential equations
G. Metafune, C. Spina (2007)
Kernel estimates for a class of Schrödinger semigroupsJournal of Evolution Equations, 7
G. Metafune, D. Pallara, M. Wacker (2002)
Feller semigroups in $${\mathbb{R}^{N}}$$ R NSemigroup Forum, 65
M. Geissert, Horst Heck, Matthias Hieber (2006)
L p -theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle, 2006
P. Civin, N. Dunford, J. Schwartz (1960)
Linear Operators. Part I: General Theory.American Mathematical Monthly, 67
J. Donaldson, Thore Johnsen, R. Mehra (1990)
On the term structure of interest ratesJournal of Economic Dynamics and Control, 14
G. Metafune, C. Spina (2011)
Heat Kernel estimates for some elliptic operators with unbounded diffusion coefficientsarXiv: Analysis of PDEs
E. Ouhabaz (2004)
Analysis of Heat Equations on Domains
M. Freidlin (2004)
Some Remarks on the Smoluchowski–Kramers ApproximationJournal of Statistical Physics, 117
(2000)
L2 theory for the operator + (k × x) · ∇ in exterior domains
F. Smithies (1954)
Linear OperatorsNature, 174
G. Metafune, C. Spina (2008)
An Integration by Parts Formula in Sobolev SpacesMediterranean Journal of Mathematics, 5
W. Arendt, A. Grabosch, G. Greiner, Ulrich Moustakas, R. Nagel, U. Schlotterbeck, U. Groh, H. Lotz, F. Neubrander (1986)
One-parameter Semigroups of Positive Operators
N. Okazawa (1984)
An L p theory for Schrödinger operators with nonnegative potentialsJournal of The Mathematical Society of Japan, 36
G. Metafune, D. Pallara, M. Wacker (2002)
Feller semigroups on RNSemigroup Forum, 65
F. Black, Myron Scholes (1973)
The Pricing of Options and Corporate LiabilitiesJournal of Political Economy, 81
G. Metafune, C. Spina (2012)
Elliptic operators with unbounded diffusion coefficients in L p spacesAnn. Scuola Norm. Sup. Pisa, Classe Scienze (5), 11
L. Lorenzi, M. Bertoldi (2006)
Analytical Methods for Markov Semigroups
E. Davies (1989)
Heat kernels and spectral theory
E. Ouhabaz, A. Rhandi (2012)
Kernel and eigenfunction estimates for some second order elliptic operatorsJournal of Mathematical Analysis and Applications, 387
M. Brennan, Eduardo Schwartz (1980)
Analyzing Convertible BondsJournal of Financial and Quantitative Analysis, 15
Tobias Hansel, A. Rhandi (2010)
The Oseen-Navier-Stokes flow in the exterior of a rotating obstacle: The non-autonomous casearXiv: Analysis of PDEs
G. Cupini, S. Fornaro (2004)
Maximal regularity in $L^p(\Bbb R^N)$ for a class of elliptic operators with unbounded coefficientsDifferential and Integral Equations
P. Wilmott, J. Dewynne, S. Howison (1994)
Option pricing: Mathematical models and computation
D. Addona (2014)
A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton–Jacobi–Bellman Type and Applications to Optimal ControlApplied Mathematics & Optimization, 72
F. Olver (1974)
Asymptotics and Special Functions
G. Metafune, C. Spina (2010)
Elliptic operators with unbounded diffusion coefficients in Lp spacesarXiv: Analysis of PDEs
A. Lunardi (2003)
Analytic Semigroups and Optimal Regularity in Parabolic Problems
We consider the Schrödinger type operator $${\mathcal{ A}=(1+|x|^{\alpha})\Delta-|x|^{\beta}}$$ A = ( 1 + | x | α ) Δ - | x | β , for $${\alpha\in (0,2)}$$ α ∈ ( 0 , 2 ) and $${\beta\ge 0}$$ β ≥ 0 . We prove that, for any $${p\in (1,\infty)}$$ p ∈ ( 1 , ∞ ) , the minimal realization of operator $${\mathcal{A}}$$ A in $${L^p(\mathbb{R}^{N})}$$ L p ( R N ) generates a strongly continuous analytic semigroup $${(T_p(t))_{t\ge 0}}$$ ( T p ( t ) ) t ≥ 0 . For α ∈ (0,2) and β ≥ 2, we then prove some upper estimates for the heat kernel k associated with the semigroup ( T p ( t )) t ≥0 . As a consequence, we obtain an estimate for large | x | of the eigenfunctions of $${\mathcal{A}}$$ A . Finally, we extend such estimates to a class of divergence type elliptic operators.
Journal of Evolution Equations – Springer Journals
Published: Mar 1, 2015
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