Explicit formulas to the solutions of Dirichlet problem for equations arising in geometry and physics. (English) Zbl 1340.35044
This paper deals with explicit formulas to the radial solutions of Liouville type semilinear elliptic partial differential equations and studies the corresponding Dirichlet problem with constant boundary data in a circle and in an annulus. It is concerned with the equations of two dimensional minimal surfaces in \( {\mathbf R}^{3} \) and \( {\mathbf R}^{4} \), the mean-field equation and others. Due to the exponential nonlinearity, the solutions can develop logarithmic singularities.
Reviewer: Angela Slavova (Sofia)
MSC:
35J60 | Nonlinear elliptic equations |
53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
35J25 | Boundary value problems for second-order elliptic equations |
35B07 | Axially symmetric solutions to PDEs |