Exponential estimates of solutions of parabolic pseudodifferential equations with discontinuous and growing symbols

Ya Lutsky, V. S. Rabinovich

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Abstract

Let Ω′⊂Rnbe an open set, and Ω+= R+×Ω′ where R+={fx0:x0} We consider pseudodifferential operators in domain Ω+with double symbols which have singularities near R+×τΩ′ and super exponential growths at infinity. We suppose that symbols have analytic extension with respect to the variable dual to the time in the lower complex half-plane. We construct the theory of invertibility of such operators in weighted Sobolev spaces with weights connected with growths of symbols. We give applications to estimates of the fundamental solutions of such operators, in particular, to the heat equations with singular potentials of power, exponential and super exponential growths. © 2009 Taylor & Francis.
Original languageAmerican English
Pages (from-to)757-778
Number of pages679
JournalComplex Variables and Elliptic Equations
DOIs
StatePublished - 1 Aug 2009

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Exponential Growth
Estimate
Sobolev spaces
Singular Potential
Weighted Sobolev Spaces
Invertibility
Pseudodifferential Operators
Operator
Fundamental Solution
Half-plane
Open set
Heat Equation
Mathematical operators
Infinity
Singularity
Hot Temperature

Cite this

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abstract = "Let Ω′⊂Rnbe an open set, and Ω+= R+×Ω′ where R+={fx0:x0} We consider pseudodifferential operators in domain Ω+with double symbols which have singularities near R+×τΩ′ and super exponential growths at infinity. We suppose that symbols have analytic extension with respect to the variable dual to the time in the lower complex half-plane. We construct the theory of invertibility of such operators in weighted Sobolev spaces with weights connected with growths of symbols. We give applications to estimates of the fundamental solutions of such operators, in particular, to the heat equations with singular potentials of power, exponential and super exponential growths. {\circledC} 2009 Taylor & Francis.",
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Exponential estimates of solutions of parabolic pseudodifferential equations with discontinuous and growing symbols. / Lutsky, Ya; Rabinovich, V. S.

In: Complex Variables and Elliptic Equations, 01.08.2009, p. 757-778.

Research output: Contribution to journalArticleResearchpeer-review

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