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
Y1 - 2009/8
N2 - Let Ω′⊂Rn be 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.
AB - Let Ω′⊂Rn be 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.
KW - Parabolic differential operators with growing coefficients
KW - Parabolic pseudodifferential operators with double symbols
KW - Weighted estimates of solutions of the homogeneous Cauchy problem
UR - http://www.scopus.com/inward/record.url?scp=70449631478&partnerID=8YFLogxK
U2 - 10.1080/17476930903030036
DO - 10.1080/17476930903030036
M3 - Artículo
SN - 1747-6933
VL - 54
SP - 757
EP - 778
JO - Complex Variables and Elliptic Equations
JF - Complex Variables and Elliptic Equations
IS - 8
ER -