Mathematical analysis of a constrained parabolic free boundary problem describing droplet motion on a surface Seiro OmataKarel Svadlenka 35K5535R3547J30partial differential equation of parabolic typeintegral constraintfree boundarydiscrete Morse flowvariational method A parabolic free boundary problem with an obstacle and a volume constraint is analyzed. The equation models slow motion of droplets on nonhomogeneous surfaces. We show existence and H\"older continuity of a unique weak solution by a combination of smoothing and a variational method called discrete Morse flow. This method can be directly applied to numerical computation. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3672 10.1512/iumj.2009.58.3672 en Indiana Univ. Math. J. 58 (2009) 2073 - 2102 state-of-the-art mathematics http://iumj.org/access/