Existence, regularity and boundary behaviour of bounded variation solutions of a one-dimensional capillarity equation
Existence, regularity and boundary behaviour of bounded variation solutions of a one-dimensional capillarity equation
We discuss existence and regularity of bounded variation solutions of the Dirichlet problem for the one-dimensional capillarity-type equation\begin{equation*}\Big( u'/{ \sqrt{1+{u'}^2}}\Big)'= f(t,u) \quad \hbox{ in } {]-r,r[},\qquadu(-r)=a, \, u(r) = b.\end{equation*}We prove interior regularity of solutions and we obtain a precise description of their boundary behaviour. This is achieved by a …