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 2.- [30] A note on harmonic functions and a hydrodynamical application.- [31] A theory of terminals and the reflection laws of partial differential equations.- [32] Asymptotic developments at the confluence of boundary conditions.- [33] Axially symmetric cavitational flow.- [34] On steady free surface flow in a gravity field.- [34A] An introduction to Riemann's Work.- [35] Extension of Huyghen's principle to the ultrahyperbolic equation.- [36] On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables.- [37] On the relations governing the boundary values of analytic functions of two complex variables.- [38] An example of a smooth linear partial differential equation without solution.- [39] On linear difference-differential equations with constant coefficients.- [40] Composition of solutions of linear partial differential equations in two independent variables.- [41] On the reflection laws of second order differential equations in two independent variables.- [42] On hulls of holomorphy.- [43] Atypical partial differential equations.- [44] Uniqueness of water waves on a sloping beach.- [47] On the definiteness of quadratic forms which obey conditions of symmetry.- [48] On the extension of harmonic functions in three variables.- [49] The wave equation as limit of hyperbolic equations of higher order.- [50] Sulla riflessione delle funzioni armoniche di 3 variablili.- [51] On a variational problem with inequalities on the boundary.- [52] On the nonvanishing of the jacobian of a homeomorphism by harmonic gradients..- [53] About the Hessian of a spherical harmonic.- [54] On the regularity of the solution of a variational inequality.- [55] On a minimumproblem for superharmonic functions.- [56] On a refinement of Evans' law in potential theory.- [57] On the partial regularity of certain superharmonics.- [58] On the smoothness of superharmonics which solve a minimum problem.- [60] On existence and smoothness of solutions of some non-coercive variational inequalities.- [61] On the coincidence set in variational inequalities.- [62] On the nature of the boundary separating two domains with different regimes.- [63] On analyticity in homogeneous first order partial differential equations.- [64] On the boundary behavior of holomorphic mappings.- [65] On the minimum number of domains in which the nodal lines of spherical harmonics divide the sphere.- [67] An inversion of the obstacle problem and its explicit solution.- [68] Expansion of solutions of t'Hooft's equation. A study in the confluence of analytic boundary conditions.- [69] On conjugate solutions of certain partial differential equations.- [70] Über die Darstellung ebener Kurven mit Doppelpunkten.- [71] On free boundary problems in two dimensions.- [72] On the analyticity of minimal surfaces at movable boundaries of prescribed length.- [73] On atypical variational problems.