The Dirichlet problem with non-compact boundary.
The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces
Let p be a real number greater than one and let X be a locally compact, noncompact metric measure space that satisfies certain conditions. The p-Royden and p-harmonic boundaries of X are constructed by using the p-Royden algebra of functions on X and a Dirichlet type problem is solved for the p-Royden boundary. We also characterize the metric measure spaces whose p-harmonic boundary is empty.
The Robin problem in potential theory (Preliminary communication)
The third boundary value problem in potential theory
The third boundary value problem in potential theory for domains with a piecewise smooth boundary
The paper investigates the third boundary value problem for the Laplace equation by the means of the potential theory. The solution is sought in the form of the Newtonian potential (1), (2), where is the unknown signed measure on the boundary. The boundary condition (4) is weakly characterized by a signed measure . Denote by the corresponding operator on the space of signed measures on the boundary of the investigated domain . If there is such that the essential spectral radius of is...
Théorème de Keldych dans la théorie axiomatique de Bauer des fonctions harmoniques
Théorie du potentiel dans les domaines lipschitziens, d'après G. C. Verchota
Transformation of Three-Dimensional Regions onto Rectangular Regions by Elliptic Systems.