Counterexample to the convexity of level sets of solutions to the mean curvature equation
The convexity of level sets of solutions to the mean curvature equation is a long standing open problem. In this paper we give a counterexample to it.
Counterexample to the regularity of weak solution of elliptic systems
Counter-Examples to Boundary Estimates for Two-Dimensional Elliptic Systems.
Counterexamples to Some Conjectures on the Number of Solutions on Nonlinear Equations.
Critical groups computations on a class of Sobolev Banach spaces via Morse index
Critical Neumann problem for nonlinear elliptic systems in exterior domains.
Critical Neumann problem with competing Hardy potentials.
Critical nonlinear elliptic equations with singularities and cylindrical symmetry
Motivated by a problem arising in astrophysics we study a nonlinear elliptic equation in RN with cylindrical symmetry and with singularities on a whole subspace of RN. We study the problem in a variational framework and, as the nonlinearity also displays a critical behavior, we use some suitable version of the Concentration-Compactness Principle. We obtain several results on existence and nonexistence of solutions.
Critical point theory for nonsmooth energy functionals and applications.
Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case
Critical points of a variant of the Ambrosio-Tortorelli functional, for which non-zero Dirichlet boundary conditions replace the fidelity term, are investigated. They are shown to converge to particular critical points of the corresponding variant of the Mumford-Shah functional; those exhibit many symmetries. That Dirichlet variant is the natural functional when addressing a problem of brittle fracture in an elastic material.
Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case
Critical points of a variant of the Ambrosio-Tortorelli functional, for which non-zero Dirichlet boundary conditions replace the fidelity term, are investigated. They are shown to converge to particular critical points of the corresponding variant of the Mumford-Shah functional; those exhibit many symmetries. That Dirichlet variant is the natural functional when addressing a problem of brittle fracture in an elastic material.
Critical points of embeddings of into Orlicz spaces
Critical singular problems on unbounded domains.
Criticality conditions for a finite homogenized natural-uranium fueled reactor with prescribed thermal neutron flux
Curvature estimates for minimal hypersurfaces in singular spaces.
Das Verhalten von Lösungen semilinearer elliptischer Systeme an Ecken eines Gebietes.
Decaying Entire Positive Solutions of Quasilinear Elliptic Equations.
Decaying positive entire solutions of the -Laplacian
Differentiability and partial Hölder continuity of the solutions of non-linear elliptic systems of order with quadratic growth
Differentiability for minimizers of anisotropic integrals
We consider a function , , minimizing the integral , , where , or some more general functional with the same behaviour; we prove the existence of second weak derivatives and .