Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues
We prove existence and bifurcation results for a semilinear eigenvalue problem in , where the linearization — has no eigenvalues. In particular, we show...
Blow-Up of Solutions of Nonlinear Wave Equations in Three Space Dimensions.
Bounding the degree of solutions to Pfaff equations
We study hypersurfaces of complex projective manifolds which are invariant by a foliation, or more generally which are solutions to a Pfaff equation. We bound their degree using classical results on logarithmic forms.
-estimates for the Cauchy-Riemann equations on certain weakly pseudoconvex domains
Classification of differential invariant submodels.
Classification of Monge-Ampère equations with two variables
This paper deals with the classification of hyperbolic Monge-Ampère equations on a two-dimensional manifold. We solve the local equivalence problem with respect to the contact transformation group assuming that the equation is of general position nondegenerate type. As an application we formulate a new method of finding symmetries. This together with previous author's results allows to state the solution of the classical S. Lie equivalence problem for the Monge-Ampère equations.
Cohomological approach to Poisson structures on nonlinear evolution equations.
Comparison of Some Solution Concepts for Linear First-order Hyperbolic Differential Equations With Non-smooth Coefficients
Comparison theorems for a class of first order Hamilton-Jacobi equations
Conditions de Levi pour le problème de Cauchy pour une classe d'équations hyperboliques à caractéristique triples
Consequences of symmetries on the analysis and construction of turbulence models.
Conservation laws for equations related to soil water equations.
Contact geometry of hyperbolic equations of generic type.
Contact geometry of hyperbolic Monge-Ampére equations.
Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions
We study the geometry of multidimensional scalar order PDEs (i.e. PDEs with independent variables), viewed as hypersurfaces in the Lagrangian Grassmann bundle over a -dimensional contact manifold . We develop the theory of characteristics of in terms of contact geometry and of the geometry of Lagrangian Grassmannian and study their relationship with intermediate integrals of . After specializing such results to general Monge-Ampère equations (MAEs), we focus our attention to MAEs of...
Contact integrable extensions and differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation
The method of contact integrable extensions is used to find new differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation and corresponding Bäcklund transformations.
Convex integration of non-linear systems of partial differential equations
Geometrical techniques are employed to prove a global existence theorem for -solutions to underdetermined systems of non-linear order partial differential equations, , which satisfy certain convexity conditions. The solutions are not unique, but satisfy given approximations on lower order derivatives. The main result, which includes the relative case generalizes the work of M. Gromov on non-linear first order systems.
Convexity for invariant differential operators on semisimple symmetric spaces
Correspondences between jet spaces and PDE systems.
Couches limites pour des problèmes mixtes hyperboliques