The work of Hans Lewy (1904--1988) has touched nearly every significant area of functional analysis and has had a profound influence in the direction of applied mathematics and partial differential equations from the late 1920s. Famous for his originality and ingenuity, Lewy illustrated and revealed fundamental principles on the theory of partial differential equations, in particular, on elliptic equations and free boundary problems. The papers presented in this two-volume set represent a selection of his best work and are augmented by commentary from his students, colleagues, and family.

Inhalt
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.