We study the spectrum of phase transitions with prescribed mean curvature in Riemannian manifolds. These are solutions to an inhomogeneous semilinear elliptic PDE that give rise diffuse objects (varifolds) limit hypersurfaces, possibly singularities, whose is determined by "prescribed curvature" function and limiting multiplicity. establish upper bounds for eigenvalues problem, as well more sub...

Surface representation as a boundary-valued problem of partial differential equations (PDE) is an important topic of computer graphics and computer aided design. In existing references, various free-from surfaces were created with a fourth order PDE which is only able to meet the tangential conditions at the surface boundaries. The need for a sixth order PDE in surface modelling arises in two s...

This paper introduces a discrete scheme for mean curvature motion using a morphological image processing approach. After brieey presenting an axiomatic approach of image processing and the mean curvature PDE, the properties of the proposed scheme are studied, in particular consistency and convergence are proved. The applications of mean curvature motion in image denoising and form evolution are...

this paper is concerned with the study of the existence of positive solutions for a navier boundaryvalue problem involving the p-biharmonic operator; the right hand side of problem is a nonsmoothfunctional with variable parameters. the existence of at least three positive solutions is establishedby using nonsmooth version of a three critical points theorem for discontinuous functions. our resul...