Focuses on partial differential equations, dealing with nonlinear Partial Differential Equations. This title treats many 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, and more.
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. This book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.
Builds upon the basic theory of linear Partial Differential Equations (PDE). This title introduces analytical tools that include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. It develops basic differential geometrical concepts, centred about curvature.
Focusing on pseudodifferential operators, the book presents a comprehensive approach to addressing issues in linear partial differential equations. It covers key topics such as existence, uniqueness, and smoothness estimates, along with various qualitative properties. Michael Taylor provides a detailed framework for understanding and applying these operators, making it a valuable resource for those studying advanced mathematical methods in differential equations.
Pseudodifferential operators are explored as a powerful tool for addressing various challenges in linear partial differential equations. The book delves into key aspects such as existence, uniqueness, and smoothness estimates, along with other qualitative properties, providing a comprehensive framework for understanding these complex mathematical problems.