conversations.from: human
conversations.value: What could be a title for a book about Sobolev with the genre: Science & Math, Mathematics?
conversations.from: assistant
conversations.value: A title for this book could be 'Partial Differential Equations'
conversations.from: human
conversations.value: Give me a description for a book titled Partial differential equations about Banach, Largely, Geared with the genre: Science & Math, Mathematics.
conversations.from: assistant
conversations.value: This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists. Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of weak derivatives, proves various inequalities and imbedding problems, and derives smoothness theorems. Part Two concerns evolution equations in Banach space and develops the theory of semigroups. It solves the initial-boundary value problem for parabolic equations and covers backward uniqueness, asymptotic behavior, and lower bounds at infinity. The final section includes independent topics directly related to the methods and results of the previous material, including the analyticity of solutions of elliptic and parabolic equations, asymptotic behavior of solutions of elliptic equations near infinity, and problems in the theory of control in Banach space.
conversations.from: human
conversations.value: Give me a description for a book titled Partial Differential Equations about It's, I've, PDE with the genre: Science & Math, Mathematics.
conversations.from: assistant
conversations.value: 'I love this book and look forward to using it as a text in the future... It's the first truly modern approach that I've seen in a PDE text.' Maeve McCarthy, MAA Online
conversations.from: human
conversations.value: Give me the first four paragraphs for this book.
conversations.from: assistant
conversations.value: Partial differential equations
  Lin, F.H.: Analysis on singular spaces. In: Li, T.T. (ed.) Geometry, Analysis and Mathematical Physics, in Honor of Prof. Chaohao Gu, 114–126, World Scientific (1997)
  Moser, J.: On Harnack's theorem for elliptic differential equations. Comm. Pure Appl. Math. 14, 577–591 (1961)CrossRefMATHMathSciNet
  Strang, G., Fix, G.: An Analysis of the Finite Element Method. Prentice Hall, Englewood Cliffs (1973)MATH
  Zeidler, E.: Nonlinear Functional Analysis and Its Applications, vol. I–IV. Springer, New York (1984)
conversations.from: human
conversations.value: Give me three more paragraphs.
conversations.from: assistant
conversations.value: Crandall, M., Lions, P.L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277, 1–42 (1983)CrossRefMATHMathSciNet
  Frehse, J.: A discontinuous solution to a mildly nonlinear elliptic system. Math. Zeitschr. 134, 229–230 (1973)CrossRefMATHMathSciNet
  Friedman, A.: Partial Differential Equations of Parabolic Type. Prentice Hall, Englewood Cliffs (1964)MATH
conversations.from: human
conversations.value: Reverse the sentences.
conversations.from: assistant
conversations.value: Prentice Hall, Englewood Cliffs (1964)MATH.: Partial Differential Equations of Parabolic Type. 134, 229–230 (1973)CrossRefMATHMathSciNet
  Friedman, A. Zeitschr. Math.: A discontinuous solution to a mildly nonlinear elliptic system. 277, 1–42 (1983)CrossRefMATHMathSciNet
  Frehse, J. Soc. Math. Amer. Trans.: Viscosity solutions of Hamilton-Jacobi equations.L., Lions, P.Crandall, M
conversations.from: human
conversations.value: Give me the last five paragraphs.
conversations.from: assistant
conversations.value: Ladyzhenskya, O.A., Ural'tseva, N.N.: Linear and Quasilinear Elliptic Equations. Nauka, Moskow, 1964 (in Russian); English translation: Academic Press, New York, 1968, 2nd Russian edition 1973
  Lin, F.H.: Analysis on singular spaces. In: Li, T.T. (ed.) Geometry, Analysis and Mathematical Physics, in Honor of Prof. Chaohao Gu, 114–126, World Scientific (1997)
  Moser, J.: On Harnack's theorem for elliptic differential equations. Comm. Pure Appl. Math. 14 , 577–591 (1961)
  Strang, G., Fix, G.: An Analysis of the Finite Element Method. Prentice Hall, Englewood Cliffs (1973)
  Zeidler, E.: Nonlinear Functional Analysis and Its Applications, vol. I–IV. Springer, New York (1984)