00000cmm a22000004a 4500 UP-99796217611212478 Buklod 20230215085534.0 m go j cr |n |||auu|a 101109s2011 xxu u eng d 9781441970497 (eBook) 1441970495 (eBook) (iLib)UPD-00215704251 DLC DML eng DMLUC QA 374 T39 2011 pt.IIIeb Taylor, Michael Eugene 1946- Partial differential equations III nonlinear equations [electronic resource] Michael E. Taylor. 2nd ed. New York Springer 2011. 1 online resource (xxii, 715 p.) ill. Applied mathematical sciences v. 117 IP-based subscription, access limited to within on campus computer network. Access via Electronic Resources of the UPD University Library Website. The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L^p Sobolev spaces, Holder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. In this second edition, there are seven new sections including Sobolev spaces on rough domains, boundary layer phenomena for the heat equation, an extension of complex interpolation theory, and Navier-Stokes equations with small viscosity. In addition, several other sections have been substantially rewritten, and numerous others polished to reflect insights obtained through the use of these books over time. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.(SIAM Review, June 1998) This text provides an introduction to the theory of partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. Companion texts, which take the theory of partial differential equations further, are AMS volume 116, treating more advanced topics in linear PDE, and AMS volume 117, treating problems in nonlinear PDE. -Source other than the Library of Congress. Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Differential equations, Partial. Electronic books. SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://dx.doi.org/10.1007/978-1-4419-7049-7 FO Monograph UPD DMLR Electronic Resource