Nonlinear Potential Theory of Degenerate Elliptic Equations

Nonlinear Potential Theory of Degenerate Elliptic Equations

Author: Juha Heinonen

Publisher: Courier Dover Publications

Published: 2018-05-16

Total Pages: 417

ISBN-13: 0486830462

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A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.


Potential Theory - ICPT 94

Potential Theory - ICPT 94

Author: Josef Kral

Publisher: Walter de Gruyter

Published: 2011-10-13

Total Pages: 513

ISBN-13: 3110818574

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The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.


Fine Regularity of Solutions of Elliptic Partial Differential Equations

Fine Regularity of Solutions of Elliptic Partial Differential Equations

Author: Jan Malý

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 309

ISBN-13: 0821803352

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The primary objective of this monograph is to give a comprehensive exposition of results surrounding the work of the authors concerning boundary regularity of weak solutions of second order elliptic quasilinear equations in divergence form. The book also contains a complete development of regularity of solutions of variational inequalities, including the double obstacle problem, where the obstacles are allowed to be discontinuous. The book concludes with a chapter devoted to the existence theory thus providing the reader with a complete treatment of the subject ranging from regularity of weak solutions to the existence of weak solutions.


Variational Analysis in Sobolev and BV Spaces

Variational Analysis in Sobolev and BV Spaces

Author: Hedy Attouch

Publisher: SIAM

Published: 2014-10-02

Total Pages: 794

ISBN-13: 1611973481

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This volume is an excellent guide for anyone interested in variational analysis, optimization, and PDEs. It offers a detailed presentation of the most important tools in variational analysis as well as applications to problems in geometry, mechanics, elasticity, and computer vision.


Variational Methods in Shape Optimization Problems

Variational Methods in Shape Optimization Problems

Author: Dorin Bucur

Publisher: Springer Science & Business Media

Published: 2005-07-01

Total Pages: 232

ISBN-13: 9780817643591

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Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.


Non-Smooth and Complementarity-Based Distributed Parameter Systems

Non-Smooth and Complementarity-Based Distributed Parameter Systems

Author: Michael Hintermüller

Publisher: Springer Nature

Published: 2022-02-18

Total Pages: 518

ISBN-13: 3030793931

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Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.