Lecture Series of the Symposium on Partial Differential Equations: Held at the University of California, at Berkeley, June 20-July 1, 1955On non-linear partial differential equations, by E. Hopf.--Difference approximation to solutions of linear differential equations, an operator theoretical approach, by P.D. Lax.--A Phragmen-Lindelof principle in harmonic analysis, with applications to the separation of variables in the theory of elliptic equations, by P.D. Lax.--Partial differential equations of the elliptic type, by M.M. Schiffer. |
Contents
ON NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS | 1 |
DIFFERENCE APPROXIMATION TO SOLUTIONS OF LINEAR | 33 |
A PHRAGMENLINDELOF PRINCIPLE IN HARMONIC | 67 |
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algebra analytic function applied approximation scheme boundary condition boundary value problems compact space consider const convergence D(hr defined denote depends difference operators differential equation 2.1 Dirichlet integral domain easily eigenfunctions eigenvalue element elliptic equations elliptic operator equal estimate exists exponential fixed fluid follows Fourier coefficients functions u(y given Green's formula Green's function Green's identity harmonic function Hence holds hyperbolic identity independent inequality infinity initial value interior compact space interval Laplace's equation Lemma linear Lipschitz continuous Math Neumann's condition norm obtained parameter partial differential equation particular solutions Phragmen-Lindelöf positive proof prove respect satisfies scalar smooth solution of Lu spectral radius sphere stability Suppose surface symmetric tends to zero theorem theory tion transform translation invariant translation operator uniformly bounded University vanishes variable variational formulas vector zero Dirichlet data