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Article Contents

# 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[}, \qquad u(-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 direct and elementary approach that exploits the properties of the zero set of the right-hand side $f$ of the equation.
Mathematics Subject Classification: Primary: 34B15, 35J93; Secondary: 49Q20, 76D45.

 Citation:

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