Gaussian Estimates for Second-Order Operators with Unbounded Coefficients

We study a family of second-order differential operators with unbounded coefficients (and possibly singular). We show that such operators generate analytic semigroups on L2((0, w), ρ2dx), 0 < w ≤ ∞, where dx denotes the Lebesgue measure. The choice of the weight ρ2 will depend on the form of the considered operator and on its coefficients.

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Asymptotic behavior of solutions to elliptic and parabolic equations with unbounded coefficients of the second order in unbounded domains

Mathematische Annalen ◽

10.1007/s00208-020-02032-2 ◽

2020 ◽

Author(s):

Hideo Kozono ◽

Yutaka Terasawa ◽

Yuta Wakasugi

Keyword(s):

Asymptotic Behavior ◽

Parabolic Equations ◽

Unbounded Domains ◽

Second Order ◽

Asymptotic Behavior Of Solutions ◽

Unbounded Coefficients ◽

Elliptic And Parabolic Equations

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Cores of Second Order Differential Linear Operators with Unbounded Coefficients on ℝN

Semigroup Forum ◽

10.1007/s00233-004-0171-8 ◽

2005 ◽

Vol 70 (2) ◽

pp. 278-295 ◽

Cited By ~ 5

Author(s):

A. A. Albanese ◽

E. Mangino

Keyword(s):

Second Order ◽

Linear Operators ◽

Unbounded Coefficients

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Conditional oscillation of Euler type half-linear differential equations with unbounded coefficients

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/012.2015.1323 ◽

2016 ◽

Vol 53 (1) ◽

pp. 22-41

Author(s):

Jaroslav Jaroš ◽

Michal Veselý

Keyword(s):

Differential Equations ◽

Second Order ◽

Oscillation Criterion ◽

Linear Differential Equations ◽

Unbounded Coefficients ◽

Conditional Oscillation ◽

Linear Differential ◽

Oscillation Constant ◽

Oscillatory Properties

The oscillatory properties of half-linear second order Euler type differential equations are studied, where the coefficients of the considered equations can be unbounded. For these equations, we prove an oscillation criterion and a non-oscillation one. We also mention a corollary which shows how our criteria improve the known results. In the corollary, the criteria give an explicit oscillation constant.

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Asymptotic behavior of solutions of second order parabolic partial differential equations with unbounded coefficients

Journal of Differential Equations ◽

10.1016/0022-0396(80)90036-4 ◽

1980 ◽

Vol 35 (3) ◽

pp. 407-428 ◽

Cited By ~ 7

Author(s):

Chris Cosner

Keyword(s):

Asymptotic Behavior ◽

Partial Differential Equations ◽

Differential Equations ◽

Second Order ◽

Parabolic Partial Differential Equations ◽

Asymptotic Behavior Of Solutions ◽

Unbounded Coefficients ◽

Partial Differential

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Sharp upper bounds for the density of some invariant measures

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210508000498 ◽

2009 ◽

Vol 139 (6) ◽

pp. 1145-1161 ◽

Cited By ~ 6

Author(s):

Simona Fornaro ◽

Nicola Fusco ◽

Giorgio Metafune ◽

Diego Pallara

Keyword(s):

Markov Processes ◽

Invariant Measures ◽

Differential Operators ◽

Upper Bounds ◽

Second Order ◽

Unbounded Coefficients ◽

Elliptic Differential Operators

We prove sharp upper bounds for invariant measures of Markov processes in ℝN associated with second-order elliptic differential operators with unbounded coefficients.

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