Everywhere regularity theorems for mappings which minimize -energy
Evolution differential equations in Fréchet sequence spaces
We consider evolution differential equations in Fréchet spaces with unconditional Schauder basis, and construct a version of the majorant functions method to obtain existence theorems for Cauchy problems. Applications to PDE are also considered.
Évolution d'une onde simple pour des équations non-linéaires générales
Evolution of convex entire graphs by curvature flows
We consider the evolution of an entire convex graph in euclidean space with speed given by a symmetric function of the principal curvatures. Under suitable assumptions on the speed and on the initial data, we prove that the solution exists for all times and it remains a graph. In addition, after appropriate rescaling, it converges to a homothetically expanding solution of the flow. In this way, we extend to a class of nonlinear speeds the well known results of Ecker and Huisken for the mean curvature...
Evolution of Eresmann's jet theory
Evolution of hypersurfaces by their curvature in Riemannian manifolds.
Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials.
Examples from the calculus of variations. I. Nondegenerate problems
The criteria of extremality for classical variational integrals depending on several functions of one independent variable and their derivatives of arbitrary orders for constrained, isoperimetrical, degenerate, degenerate constrained, and so on, cases are investigated by means of adapted Poincare-Cartan forms. Without ambitions on a noble generalizing theory, the main part of the article consists of simple illustrative examples within a somewhat naive point of view in order to obtain results resembling...
Examples from the calculus of variations. II. A degenerate problem
Continuing the previous Part I, the degenerate first order variational integrals depending on two functions of one independent variable are investigated.
Examples from the calculus of variations. III. Legendre and Jacobi conditions
We will deal with a new geometrical interpretation of the classical Legendre and Jacobi conditions: they are represented by the rate and the magnitude of rotation of certain linear subspaces of the tangent space around the tangents to the extremals. (The linear subspaces can be replaced by conical subsets of the tangent space.) This interpretation can be carried over to nondegenerate Lagrange problems but applies also to the degenerate variational integrals mentioned in the preceding Part II.
Examples from the calculus of variations. IV. Concluding review
Variational integrals containing several functions of one independent variable subjected moreover to an underdetermined system of ordinary differential equations (the Lagrange problem) are investigated within a survey of examples. More systematical discussion of two crucial examples from Part I with help of the methods of Parts II and III is performed not excluding certain instructive subcases to manifest the significant role of generalized Poincaré-Cartan forms without undetermined multipliers....
Examples of Harmonic Maps from Disks to Hemisphere.
Examples of infinite dimensional isoparametric submanifolds.
Exemples d'applications holomorphes d'indice un
Nous construisons une famille de surfaces de Riemann hyperelliptiques, de genre variable, munies de fonctions méromorphes de degré deux et d’indice un, ce qui apporte une réponse positive à une conjecture de S. Montiel et A. Ros.
Existence and asymptotic behavior of solutions for weighted -Laplacian system multipoint boundary value problems in half line.
Existence and asymptotics for selfdual periodic vortices of topological-type
Existence and concentration of solutions for a -Laplace equation with potentials in .
Existence and construction of Vessiot connections.
Existence and density results for retarded subdifferential evolution inclusions
In this paper we study Cauchy problems for retarded evolution inclusions, where the Fréchet subdifferential of a function F:Ω→R∪{+∞} (Ω is an open subset of a real separable Hilbert space) having a φ-monotone subdifferential of oder two is present. First we establish the existence of extremal trajectories and we show that the set of these trajectories is dense in the solution set of the original convex problem for the norm topology of the Banach space C([-r, T₀], Ω) ("strong relaxation theorem")....
Existence and multiplicity of nontrivial solutions for double resonance semilinear elliptic problems.