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Full Description
The work of Hans Lewy (1904-1988) has had a profound influence in the direc tion of applied mathematics and partial differential equations, in particular, from the late 1920s. We are all familiar with two of the particulars. The Courant-Friedrichs Lewy condition (1928), or CFL condition, was devised to obtain existence and ap proximation results. This condition, relating the time and spatial discretizations for finite difference schemes, is now universally employed in the simulation of solutions of equations describing propagation phenomena. His example of a linear equation with no solution (1957), with its attendant consequence that most equations have no solution, was not merely an unexpected fact, but changed the viewpoint of the entire field. Lewy made pivotal contributions in many other areas, for example, the regu larity theory of elliptic equations and systems, the Monge-Ampere Equation, the Minkowski Problem, the asymptotic analysis of boundary value problems, and sev eral complex variables. He was among the first to study variational inequalities. In much of his work, his underlying philosophy was that simple tools of function theory could help us understand the essential concepts embedded in an issue, although at a cost in generality. This was extremely successful.
Contents
to Volume 1.- [1] Über einen Ansatz zur numerischen Lösung von Randwertproblemen.- [3] Über den analytischen Charakter der Lösungen elliptischer Differentialgleichungen..- [4] Über die Methode der Differenzengleichungen zur Lösung von Variations- und Randwertproblemen.- [5] Über das Anfangswertproblem bei einer hyperbolischen nichtlinearen partiellen Differentialgleichung zweiter Ordnung mit zwei unabhängigen Veränderlichen.- [6] Über die Eindeutigkeit und das Abhängigkeitsgebiet der Lösungen beim Anfangswertproblem linearer hyperbolischer Differentialgleichungen.- [7] On the Partial Difference Equations of Mathematical Physics.- [8] Das Anfangswertproblem einer beliebigen nichtlinearen hyperbolischen Differentialgleichung beliebiger Ordnung in zwei Variablen: Existenz, Eindeutigkeit und Abhängigkeitsbereich der Lösung.- [9] Neuer Beweis des analytischen Charakters der Lösungen elliptischer Differentialgleichungen.- [10] Sulla unicità della soluzione del problema di Cauchy per un'equaztione ellitica del secondo ordine in due variabili.- [11] Eindeutigkeit der Lösung des Anfangsproblems einer elliptischen Differentialgleichungen zweiter Ordnung in zwei Veränderlichen.- [12] Über fortsetzbare Anfangsbedingungen bei hyperbolischen Differentialgleichungen in drei Veränderlichen.- [13] On convergence in length.- [14] A priori limitations for solutions of Monge-Ampère equations.- [15] Generalized integrals and differential equations.- [16] On the non-vanishing of the Jacobian in certain one-to-one mappings.- [17] A priori limitations for solutions of Monge-Ampère equations, II.- [18] On the existence of a closed convex surface realizing a given Riemannian metric.- [19] On differential geometry in the large, I (Minkowski's Problem).- [20] Generalizedintegrals and differential equations.- [21] A property of spherical harmonics.- [23] Water waves on sloping beaches.- [24] The dock problem.- [25] On the convergence of solutions of difference equations, Studies and Essays.- [26] Developments at the confluence of analytic boundary conditions.- [27] Developments at the confluence of analytic boundary conditions.- [28] On minimal surfaces with partially free boundary.- [29] On the boundary behavior of minimal surfaces.
