L. C. Evans, Partial Differential Equations , Graduate Studies in Mathematics, Volume 19, AMS.
Some other references are the following.
An introduction to elliptic and parabolic PDEs is in:
N. V. Krylov, Lectures on Elliptic and Parabolic Partial Differential Equations in Holder Spaces , Graduate Studies in Mathematics 12, AMS Providence RI, 1996.
A standard reference on elliptic PDEs is:
D. Gilbarg, and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order , Springer-Verlag, New York, 1983.
For a readable account of maximum principles, see:
M. H. Protter, and H. F. Weinberger, Maximum Principles in Differential Equations , Prentice-Hall, Englewood Cliffs, 1967.
Spherical means are discussed in:
F. John, Plane Waves and Spherical Means Applied to Partial Differential Equations , Springer-Verlag, New York, 1981.
For the Tychonoff solution of the heat equation, and Lewy's example of a PDE without solutions, see:
F. John, Partial Differential Equations , 4th ed., Springer-Verlag, New York, 1982.
The Cauchy-Kowalewski theorem is proved in:
P. Garabedian, Partial Differential Equations , John Wiley & Sons, New York, 1964.
Characteristic surfaces of hyperbolic PDEs are described in:
R. Courant, and D. Hilbert, Methods of Mathematical Physics , Vol. 2, Interscience, New York, 1961.
For a thorough account of distribution theory and the Fourier transform, see:
L. Hormander, The Analysis of Linear Partial Differential Operators , Vol. 1, Springer-Verlag, Berlin, 1983.
For the solution of linear initial value problems by the Fourier transform, and the Hadamard-Petrowsky dichotomy, see:
J. Rauch, Partial Differential Equations , Springer-Verlag, New York, 1991.
For an introduction to the physical aspects of Burger's equations, see:
G. Whitham, Linear and Nonlinear Waves , Wiley-Interscience, New York, 1973.
An account of the mathematical theory of conservation laws is in
J. Smoller, Shock Waves and Reaction-Diffusion Equations , Springer-Verlag, New York, 1983.
For the numerical solution of conservation laws, see
R. J. LeVeque, Numerical Methods for Conservation Laws , Birkhauser, Basel, 1992.
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