Necessary and sufficient conditions for the local solvability in hyperfunctions of a class of systems of complex vector fields.
Necessary Conditions for Multiple Integral Problem in the Calculus of Variations.
Negative Curvature and Embedded Eigenvalues.
Nets on a Riemannian manifold and finite-dimensional approximations of the Laplacian [Book]
Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces
We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space.
New boson realizations of quantum groups
New bounds for the principal Dirichlet eigenvalue of planar regions.
New estimates for elliptic equations and Hodge type systems
We establish new estimates for the Laplacian, the div-curl system, and more general Hodge systems in arbitrary dimension , with data in . We also present related results concerning differential forms with coefficients in the limiting Sobolev space .
New examples of biharmonic maps in spheres
We give some new methods to construct nonharmonic biharmonic maps in the unit n-dimensional sphere 𝕊ⁿ.
New Examples of harmonic diffeomorphisms of the hyperbolic plane onto itself.
New inequalities for the jacobian
New operators on jet spaces
New results concerning the number of small eigenvalues on Riemann surfaces.
New results on the classical problem of Plateau on the existence of many solutions
New solutions of equations on
New versions of curvature and torsion formulas for the complete lifting of a linear connection to Weil bundles
New versions of Slovák’s formulas expressing the covariant derivative and curvature of the linear connection are presented.
New weighted Poincaré-type inequalities for differential forms.
Newton and conjugate gradient for harmonic maps from the disc into the sphere
We compute numerically the minimizers of the Dirichlet energyamong maps from the unit disc into the unit sphere that satisfy a boundary condition and a degree condition. We use a Sobolev gradient algorithm for the minimization and we prove that its continuous version preserves the degree. For the discretization of the problem we use continuous finite elements. We propose an original mesh-refining strategy needed to preserve the degree with the discrete version of the algorithm (which is a preconditioned...
Newton and conjugate gradient for harmonic maps from the disc into the sphere
We compute numerically the minimizers of the Dirichlet energy among maps from the unit disc into the unit sphere that satisfy a boundary condition and a degree condition. We use a Sobolev gradient algorithm for the minimization and we prove that its continuous version preserves the degree. For the discretization of the problem we use continuous P1 finite elements. We propose an original mesh-refining strategy needed to preserve the degree with the discrete version of the algorithm (which...
Newton's methods from a geometric point of view.