$\mathcal {R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type

Released on by Robert Denk
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  • $\mathcal {R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type Book Detail

  • Author : Robert Denk
  • Release Date : 2003
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 130
  • ISBN 13 : 0821833782
  • File Size : 22,22 MB
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$\mathcal {R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type by Robert Denk PDF Summary

Book Description: The property of maximal $L_p$-regularity for parabolic evolution equations is investigated via the concept of $\mathcal R$-sectorial operators and operator-valued Fourier multipliers. As application, we consider the $L_q$-realization of an elliptic boundary value problem of order $2m$ with operator-valued coefficients subject to general boundary conditions. We show that there is maximal $L_p$-$L_q$-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.

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Yang-Mills Measure on Compact Surfaces

Yang-Mills Measure on Compact Surfaces

File Size : 16,16 MB
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In this memoir we present a new construction and new properties of the Yang-Mills measure in two dimensions. This measure was first introduced for the needs of