A generalization of Schauder's theorem and its application to Cauchy-Kovalevskaya problem.
A Holmgren type theorem for partial differential equations whose coefficients are Gevrey functions.
A sufficient condition for existence of real analytic solutions of P.D.E. with constant coefficients, in open sets of
Abstract version of the Cauchy-Kowalewski problem
We consider an abstract version of the Cauchy-Kowalewski Problem with the right hand side being free from the Lipschitz type conditions and prove the existence theorem.
An abstract non-linear Cauchy-Kowalewski theorem and its proof by a contraction-mapping principle
Analytic solution of an initial-value problem from Stokes flow with free boundary.
Cauchy-Kowalewski extension theorems and representations of analytic functionals acting over special classes of real n-dimensional submanifolds of
Cauchy-Kowalewski theorems in Clifford analysis : a survey
Continuous and generalized solutions of singular partial differential equations.
Convergence of formal solutions of first order singular nonlinear partial differential equations in the complex domain
We study the convergence or divergence of formal (power series) solutions of first order nonlinear partial differential equations (SE) f(x,u,Dx u) = 0 with u(0)=0. Here the function f(x,u,ξ) is defined and holomorphic in a neighbourhood of a point and . The equation (SE) is said to be singular if f(0,0,ξ) ≡ 0 . The criterion of convergence of a formal solution of (SE) is given by a generalized form of the Poincaré condition which depends on each formal solution. In the case where the formal...
Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem
We study convergence of formal power series along families of formal or analytic vector fields. One of our results says that if a formal power series converges along a family of vector fields, then it also converges along their commutators. Using this theorem and a result of T. Morimoto, we prove analyticity of formal solutions for a class of nonlinear singular PDEs. In the proofs we use results from control theory.
Ein Funktionalanalytischer Beweis des Satzes von Cauchy-Kowalewsky.
Einige Bemerkungen über eine Differenzenfunktionalgleichung.
Équations d'évolution à grand paramètre
Estimation d'opérateurs intégraux du type de Cauchy dans les échelles d'Ovsjannikov et application
On établit des estimations de l’intégrale singulière de Cauchy et des opérateurs du potentiel dans des échelles d’Ovjannikov de fonctions analytiques. Ces estimations sont utilisées pour obtenir des résultats d’existence locale en temps de solutions analytiques pour certains problèmes à frontière libre dans le plan.
Existence for elliptic equations in having lower order terms with natural growth.
Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity
In this paper, we calculate the formal Gevrey index of the formal solution of a class of nonlinear first order totally characteristic type partial differential equations with irregular singularity in the space variable. We also prove that our index is the best possible one in a generic case.
Functional differential equations of the Cauchy-Kowalewsky type.
How many are affine connections with torsion
The question how many real analytic affine connections exist locally on a smooth manifold of dimension is studied. The families of general affine connections with torsion and with skew-symmetric Ricci tensor, or symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of variables.
How many are equiaffine connections with torsion
The question how many real analytic equiaffine connections with arbitrary torsion exist locally on a smooth manifold of dimension is studied. The families of general equiaffine connections and with skew-symmetric Ricci tensor, or with symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of variables.