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E-raamat: Oblique Derivative Problems For Elliptic Equations

(Iowa State Univ Of Science & Tech, Usa)
  • Formaat: 528 pages
  • Ilmumisaeg: 26-Mar-2013
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814452342
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  • Raamatukogudele
  • Formaat: 528 pages
  • Ilmumisaeg: 26-Mar-2013
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814452342

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This book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author. Such problems also arise in many other physical situations such as the shape of a capillary surface and problems of optimal transportation. The author begins the book with basic results for linear oblique derivative problems and work through the theory for quasilinear and nonlinear problems. The final chapter discusses some of the applications. In addition, notes to each chapter give a history of the topics in that chapter and suggestions for further reading.
Pointwise Estimates; Classical Schauder Theory from a Modern
Perspective; The Miller Barrier and Some Supersolutions for Oblique
Derivative Problems; Holder Estimates for First and Second Derivatives; Weak
Solutions; Strong Solutions; Viscosity Solutions of Oblique Derivative
Problems; Pointwise Bounds for Solutions of Problems with Quasilinear
Equations; Gradient Estimates for General Form Oblique Derivative Problems;
Gradient Estimates for the Conormal Derivative Problems; Higher Order
Estimates and Existence of Solutions for Quasilinear Oblique Derivative
Problems; Oblique Derivative Problems for Fully Nonlinear Elliptic Equations.