### Abstract

Original language | American English |
---|---|

Pages (from-to) | 757-778 |

Number of pages | 679 |

Journal | Complex Variables and Elliptic Equations |

DOIs | |

State | Published - 1 Aug 2009 |

### Fingerprint

### Cite this

}

**Exponential estimates of solutions of parabolic pseudodifferential equations with discontinuous and growing symbols.** / Lutsky, Ya; Rabinovich, V. S.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Exponential estimates of solutions of parabolic pseudodifferential equations with discontinuous and growing symbols

AU - Lutsky, Ya

AU - Rabinovich, V. S.

PY - 2009/8/1

Y1 - 2009/8/1

N2 - 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.

AB - 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.

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=70449631478&origin=inward

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=70449631478&origin=inward

U2 - 10.1080/17476930903030036

DO - 10.1080/17476930903030036

M3 - Article

SP - 757

EP - 778

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

ER -