Biographical Memoirs Volume 54 (1983) / Chapter Skim
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Griffith Conrad Evans
Griffith Conrad Evans
Pages 126-155
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rat rat ;` J ~0 a 4 o
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After receiving his Ph.D., he studied from ~ 9 ~ 0 through ~ 9 ~ 2 at the University of Rome on a Sheldon Traveling Fellowship from Harvard. He began his teaching career in 1912 as assistant professor of mathematics at the newly established Rice Institute, now Rice University, in Houston, Texas.
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Professor Evans and others on the Berkeley campus recognized the importance of the fields of probability and statistics, and Professor Jerzy Neyman was brought to that campus by Evans in 1939 to organize the Statistical Laboratory. A period of rapid growth followed; by the close of World War IT the Laboratory had transformed Berkeley into one of the three principal centers of probability and statistics in the country.
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During the ensuing ten years, he contributed a great deal to the development of the general field of integral equations and more general functional equations. His principal results concerned certain integro-ctifferential equations and integral equations with singular kernels.
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The funciamental problem in potential theory is the DirichIet problem. Roughly speaking, this consists in proving the existence and uniqueness of the function U that satisfies Laplaces equation on a given domain G
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is the solution of the Dirichlet problem with boundary values g (I)
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recluces to the solution of the DirichIet problem with continuous boundary valuesf(¢)
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, which is obtained using physical considerations and so is not logically suitable for a mathematical derivation. In 1913 Lebesgue gave an example of the impossibility of the solution of the DirichIet problem.5 The region R can be obtained by revolving about the x-axis the area bounded by the curves y =e-"x, y = 0 and x = I
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= 4—JJ ~ ~ r 2) (MP ~ -3g (P ~ dS s 4 IT JJ g The first term on the right is just the solution of the Dirichlet problem with the boundary values g(M)
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Professor Evans proved that any potential function of a positive mass is superharmonic on any clomain on which it is defined. Evans also gave the simplest proof of the following theorem due to F
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A Sequence of Potentials (A Sweeping Out ProcessJ. Evans gave a simple proof that the limit of a non-decreasing bounded sequence of potential functions of positive mass each distributed on a fixed bounded closed set F is itself a potential of positive mass F
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such that {fin ~ converges weakly to a positive mass functionf on F (or a subset of F)
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Multipite Valued Harmonic Functions in Space. In I896 Sommerfelt developed a method of using multivalued harmonic functions in three space to solve certain problems in potential theory, particularly the diffraction problem for a straight line.
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Since any multiple space is, by definition, a topological space, open, closed, and connected subsets of such spaces are clefinecl and the usual theorems hoIcI. Also harmonic, superharmonic, and subharmonic functions can be clefinec!
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; this i3 For a full discussion, see Griffith Conrad Evans, "Multiply Valued Harmonic Functions. Green's Theorem," Proceedings of the National Academy of Sciences of the United States of America, 33 (1947)
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GRIFFITH CONRAD EVANS 141 is called the cost function. The consumer will buy y units of the commodity (per unit time)
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As a second theory, Evans assumes that there are two producers manufacturing amounts u ~ and u 2 of the commoctity (per unit time)
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to the case where there are n producers, each subject to a different cost and demand function, but who all set the same price p. Then the i-th producer produces ui units where the total profit is n U=Z ~i= i = I n ~ (pal i = I This will be a maximum if du; which yields d~=o or p—2Aiui—BiUi, p—Bi Hi=- a = 1~.
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A Bliss, Calculus of Variations (Washington, D.C.: Mathematical Association of America, 1925)
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GRIFFITH CONRAD EVANS 145 holds. Carrying out the differentiation with respect to t in (3)
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actresses in Italy and elsewhere cluring that period. Professor Evans was elected to the National Academy of Sciences in 1933 anti became a member of the American Academy of Arts and Sciences, the American Philosophical Society, the American Mathematical Society (vice president, 192~26; president, 1938-401; the Mathematical Association of America (vice president, 1934)
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Professor Evans married Isabel Mary John in 1917. They had three children, Griffith C
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5, 20:7-11. Sul calcolo del nucleo dell'equazione risolvente per una data equazione integrale.
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(Lectures delivered at the inauguration of the Rice Institute by Senator Vito Volterra. Translated from the Italian.)
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Functionals and their Applications Selected Topics, Including Integral Equations.
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On the approximation of functions of a real variable and on quasianalytic functions. (Lectures delivered at the Rice Institute by Charles de la Vallee Poussin.
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Soc., 36:427-33. The mixed problem for Laplace's equation in the plane discontinuous boundary values.
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Math., 11:245-58. 1936 Potentials and positively infinite singularities of harmonic functions.
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1951 Lectures of multiple valued harmonic functions in space.
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1959 Infinitely multiple valued harmonic functions in space with two branch curves of order one.
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