Existence theory in nonsmooth domains. Shape optimization, continuity of the work functional

  • Pavel Plotnikov
  • Jan Sokołowski
Part of the Monografie Matematyczne book series (MONOGRAFIE, volume 73)


In this section we employ the main stability theorem (Theorem 9.3.1) and Proposition 8.3.6 to prove that the flow problem around an obstacle has a renormalized solution for every compact obstacle. The corresponding result is given by the following theorem, which is one of the main results of this monograph.


Energy Estimate Stability Theorem Existence Theory Lebesgue Dominate Convergence Theorem Compressible Navier Stokes Equation 
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Copyright information

© Springer Basel 2012

Authors and Affiliations

  • Pavel Plotnikov
    • 1
  • Jan Sokołowski
    • 2
  1. 1.Siberian Branch of RAS Lavrentyev Institute of HydrodynamicsNovosibirskRussia
  2. 2.Institut Élie Cartan de Nancy, UMR 7502Université de Lorraine, CNRSVandœuvre-lès-NancyFrance

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