Abstract. A possible evolution of a compact hypersurface in R by mean curvature past singularities is defined via the level set flow. In the case that the initial hypersurface has positive mean curvature, we show that the Brakke flow associated to the level set flow is actually a Brakke flow with equality. We obtain as a consequence that no mass drop can occur along such a flow. As a further ap...

Variational iteration method is introduced to solve two-point boundary value problem for a second order fuzzy differential equation under generalized Hukuhara differentiability. To illustrate the ability and reliability of the method, some examples are given, revealing its effectiveness and simplicity.

Existence of minimizers for a volume constrained energy

In this work we study the sequence of variational eigenvalues of a system of resonant type involving p− and q−laplacians on Ω ⊂ R , with a coupling term depending on two parameters α and β satisfying α/p+β/q = 1. We show that the order of growth of the k eigenvalue depends on α + β, λk = O(k α+β N ).

We extend some earlier results on existence of homoclinic solutions for a class of Hamiltonian systems. We also study heteroclinic solutions. We use variational approach.

We prove an asymptotic estimate for the growth of variational eigenvalues of fractional p-Laplacian eigenvalue problems on a smooth bounded domain.

Causal variational principles on measure spaces are introduced. General existence results are proved. It is shown in examples that minimizers need not be unique. Counter examples to compactness are discussed. The existence results are applied to variational principles formulated in indefinite inner product spaces.

We apply the geometric construction of solutions of some variational problems of combinatorics to estimate the number of partitions and of plane partitions of an integer.

Brain shift, i. e. the change in configuration of the brain after opening the dura mater, is a key problem in neuronavigation. We present an approach to co-register intra-operative microscope images with preoperative MRI data to adapt and optimize intra-operative neuronavigation. The tools are a robust classification of sulci on MRI extracted cortical surfaces, guided user marking of most promi...