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中图分类法:
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O17 版次： |
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著者:
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Katzourakis, Nikos, |
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题名:
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An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L/ / , |
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载体形态:
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xii, 123 pages : illustrations (some color) ; 24 cm. |
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内容提要:
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The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE. |
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主题词:
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Calculus of variations. |
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主题词:
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Differential equations, Nonlinear. |
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主题词:
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Differential equations, Partial. |
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主题词:
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Calculus of Variations and Optimal Control; Optimization. |
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主题词:
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Partial Differential Equations. |
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索书号:
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1 |