This book gives a concise and systematic exposition on a new functional analytic method for handling a large class of nonlinear partial differential equations and systems. With important applications to the calculus of variations, nonlinear elasticity, problems of phase transitions and optimal design, it should appeal to a wide audience. The book presents introductory material and applications, and includes many mathematical examples derived from applications to materials science.
Implicit Partial Differential Equations
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Editorial Reviews
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"Provides a self-contained development of the new kind of differential equations… Includes many examples helpful in understanding the theory and is well [and] clearly written."
—Mathematical Reviews
"…Topics of the book have important applications in variational calculus, nonlinear elasticity, phase transitions, and optimal design. In particular, Part IV (Chapters 7-9) includes the singular value case, the case of potential wells, and the complex eikonal equation. A lot of background material, as viscosity solutions, quasiconvexity and related topics, piecewise polynomial approximation in Sobolev spaces, convex integration, or nonclassical Vitali-type covering theorems, is presented in the book, which makes it essentially self-contained. Most of the results are original from the authors, some results are published even first time. This makes the book a unique introduction to this new topic, and will be found useful by experts in nonlinear analysis in general and PDEs in particular, as well as by advanced graduate students in this field."
–Zentralblatt Math
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Inside This Book
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First Sentence:
In this chapter we will deal with first order scalar partial differential equations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rank one convex hull, rank one direction, one convex hulls, quasiconvex hull, boundary datum, vectorial case, convex integration, rank one convexity, proof into two steps, coercivity assumption, weak lower semicontinuity, viscosity supersolution, convex sense, viscosity subsolution, higher order case, piecewise affine, eikonal equation, coercivity condition, convex with respect, disjoint open sets, calcul des variations, gradient variable, covering theorem, relaxation property, category theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter we will deal with first order scalar partial differential equations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rank one convex hull, rank one direction, one convex hulls, quasiconvex hull, boundary datum, vectorial case, convex integration, rank one convexity, proof into two steps, coercivity assumption, weak lower semicontinuity, viscosity supersolution, convex sense, viscosity subsolution, higher order case, piecewise affine, eikonal equation, coercivity condition, convex with respect, disjoint open sets, calcul des variations, gradient variable, covering theorem, relaxation property, category theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Mac Shane New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 6
books:
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21
books
cite this book:
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- Homogenization of Multiple Integrals (Oxford Lecture Series in Mathematics and Its Applications) by Andrea Braides in Back Matter
- Partial Differential Equations (Applied Mathematical Sciences) (v. 1) by Fritz John in Front Matter
- Partial Differential Equations (Chapman & Hall/CRC Research Notes in Mathematics Series) by Joseph Wiener in Back Matter
- New York by Tama Janowitz in Back Matter
- Convex Analysis (Princeton Landmarks in Mathematics and Physics) by Ralph Tyrell Rockafellar in Back Matter
See all 6 books this book cites
- Energy Methods for Free Boundary Problems: Applications to Nonlinear PDEs and Fluid Mechanics (Progress in Nonlinear Differential Equations and Their Applications) by S.N. Antontsev in Back Matter
- Regularity Theory for Mean Curvature Flow by Klaus Ecker in Back Matter
- Free Energy and Self-Interacting Particles (Progress in Nonlinear Differential Equations and Their Applications) by Takashi Suzuki in Back Matter
- Real Analysis by Emmanuele DiBenedetto in Back Matter
- Systems of Conservation Laws: Two-Dimensional Riemann Problems (Progress in Nonlinear Differential Equations and Their Applications 38) by Yuxi Zheng in Back Matter
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