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- DescriptionNonlinear partial differential equations has become one of the main tools of mod- ern mathematical analysis; in spite of seemingly contradictory termilogy, the subject of nlinear differential equations finds its origins in the theory of linear differential equations, and a large part of functional analysis derived its inspiration from the study of linear pdes. In recent years, several mathematicians have investigated nlinear equations, particularly those of the second order, both linear and nlinear and either in divergence or ndivergence form. Quasilinear and fully nlinear differential equations are relevant classes of such equations and have been widely examined in the mathematical literature. In this work we present a new family of differential equations called implicit partial differential equations , described in detail in the introduction (c.f. Chapter 1). It is a class of nlinear equations that does t include the family of fully nlinear elliptic pdes. We present a new functional analytic method based on the Baire category theorem for handling the existence of almost everywhere solutions of these implicit equations. The results have been obtained for the most part in recent years and have important applications to the calculus of variations, nlin- ear elasticity, problems of phase transitions and optimal design; some results have t been published elsewhere.
- Author(s)Bernard Dacorogna,Paolo Marcellini
- PublisherSpringer-Verlag New York Inc.
- Date of Publication21/10/2012
- Series TitleProgress in Nonlinear Differential Equations and Their Applications
- Series Part/Volume Number37
- Place of PublicationNew York
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Notebiography
- Weight450 g
- Width155 mm
- Height235 mm
- Spine15 mm
- Edition StatementSoftcover reprint of the original 1st ed. 1999
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