A fixed point formulation of the -means algorithm and a connection to Mumford-Shah.
A free boundary problem involving limiting Sobolev exponents.
A free boundary problem with a volume penalization
A frictional contact problem for an electro-viscoelastic body.
A frictional contact problem with adhesion for viscoelastic materials with long memory
We consider a quasistatic contact problem between a viscoelastic material with long-term memory and a foundation. The contact is modelled with a normal compliance condition, a version of Coulomb's law of dry friction and a bonding field which describes the adhesion effect. We derive a variational formulation of the mechanical problem and, under a smallness assumption, we establish an existence theorem of a weak solution including a regularity result. The proof is based on the time-discretization...
A further generalization of Ky Fan's maximal inequality and its applications
A Further Note on the Exterior Capillarity Problem.
A game interpretation of the Neumann problem for fully nonlinear parabolic and elliptic equations
We provide a deterministic-control-based interpretation for a broad class of fully nonlinear parabolic and elliptic PDEs with continuous Neumann boundary conditions in a smooth domain. We construct families of two-person games depending on a small parameter ε which extend those proposed by Kohn and Serfaty [21]. These new games treat a Neumann boundary condition by introducing some specific rules near the boundary. We show that the value function converges, in the viscosity sense, to the solution...
A general approach to the existence of minimizers of one-dimensional non-coercive integrals of the calculus of variations
A General Convergence Theorem for the Reduced Gradient Method.
A general duality theorem for the Monge-Kantorovich transport problem
The duality theory for the Monge-Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be Polish and equipped with Borel probability measures μ and ν. The transport cost function c: X × Y → [0,∞] is assumed to be Borel. Our main result states that in this setting there is no duality gap provided the optimal transport problem is formulated in a suitably relaxed way. The relaxed transport problem is defined as the limiting cost of the partial transport...
A general existence theorem for differential inclusions in the vector valued case.
A General Existence Theorem for Surfaces of Constant Mean Curvature.
A general Hamilton-Jacobi framework for non-linear state-constrained control problems
The paper deals with deterministic optimal control problems with state constraints and non-linear dynamics. It is known for such problems that the value function is in general discontinuous and its characterization by means of a Hamilton-Jacobi equation requires some controllability assumptions involving the dynamics and the set of state constraints. Here, we first adopt the viability point of view and look at the value function as its epigraph. Then, we prove that this epigraph can always be described...
A general Hilbert space approach to framelets.
A general iterative algorithm for generalized mixed equilibrium problems and variational inclusions approach to variational inequalities.
A general iterative method for solving the variational inequality problem and fixed point problem of an infinite family of nonexpansive mappings in Hilbert spaces.
A general iterative method for variational inequality problems, mixed equilibrium problems, and fixed point problems of strictly pseudocontractive mappings in Hilbert spaces.
A general mountain pass principle for locating and classifying critical points
A general projection method for a system of relaxed cocoercive variational inequalities in Hilbert spaces.