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Maximal regularity in L p (R N ) for a class of elliptic operators with unbounded coefficients, Differential Integral Equations
 Di¤ erential Integral Equations
"... Abstract. Strongly elliptic differential operators with (possibly) unbounded lower order coefficients are shown to generate C0semigroups on L p (R N), 1 < p < +∞. An explicit characterization of the domain is given. 1. ..."
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Abstract. Strongly elliptic differential operators with (possibly) unbounded lower order coefficients are shown to generate C0semigroups on L p (R N), 1 < p < +∞. An explicit characterization of the domain is given. 1.
Elliptic and parabolic secondorder PDEs with growing coefficients
"... Abstract. We consider a secondorder parabolic equation in R d+1 with possibly unbounded lower order coefficients. All coefficients are assumed to be only measurable in the time variable and locally Hölder continuous in the space variables. We show that global Schauder estimates hold even in this ca ..."
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Cited by 7 (4 self)
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Abstract. We consider a secondorder parabolic equation in R d+1 with possibly unbounded lower order coefficients. All coefficients are assumed to be only measurable in the time variable and locally Hölder continuous in the space variables. We show that global Schauder estimates hold even in this case. The proof introduces a new localization procedure. Our results show that the constant appearing in the classical Schauder estimates is in fact independent of the L∞norms of the lower order coefficients. We also give a proof of uniqueness which is of independent interest even in the case of bounded coefficients.
Discreteness of the Spectrum for Some Differential Operators With Unbounded Coefficients in R^n
"... We give sufficient conditions for the discreteness of the spectrum of differential operators of the form Au = \Gamma\Deltau +hrF;rui in L 2 (R n ) where d(x) = e \GammaF (x) dx and for Schrödinger operators in L 2 (R n ). Our conditions are also necessary in the case of polynomial coeffic ..."
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Cited by 3 (1 self)
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We give sufficient conditions for the discreteness of the spectrum of differential operators of the form Au = \Gamma\Deltau +hrF;rui in L 2 (R n ) where d(x) = e \GammaF (x) dx and for Schrödinger operators in L 2 (R n ). Our conditions are also necessary in the case of polynomial coefficients.