Titlebook: Direct and Inverse Problems of Mathematical Physics; Robert P. Gilbert,Joji Kajiwara,Yongzhi S. Xu Book 2000 Springer Science+Business Med

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Quasi-Exponential Solutions for Some PDE with Coefficients of Limited Regularity,Let . be a bounded Lipshitz domain, and let . In Ω, consider an elliptic equation . with . Assume also that a is real valued and has a positive lower bound. We prove that for |ζ| sufficiently large, this equation has special quasi-exponential solutions of the form . depending on parameter ζ and such that . for any . ∈ (0,1).

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,Analytically Smoothing Effect for Schr?dinger Type Equations with Variable Coefficients,We shall investigate analytically smoothing effects of the solutions to the Cauchy problem for Schr?dinger type equations. We shall prove that if the initial data decay exponentially then the solutions become analytic with respect to the space variables. Let . > 0.

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,Boundedness of Pseudo-Differential Operators on H?rmander Spaces,fferential operators fail to be bounded on these spaces. Fourier integral operators and their global mapping properties are studied in this setting. Applications to the regularity of solutions of semilinear pseudo-differential equations on ?. are presented.

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