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Elements of the general theory of Lie-Cartan pseudogroups (including the intransitive case) are developed within the framework of infinitely prolonged systems of partial differential equations (diffieties) which makes it independent of any particular realizations by transformations of geometric object. Three axiomatic approaches, the concepts of essential invariant, subgroup, normal subgroup and factorgroups are discussed. The existence of a very special canonical composition series based on Cauchy...

On functions, whose lines of steepest descent bend proportionally to level lines

Giorgio Talenti (1983)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On linearizing systems of diffusion equations.

Sophocleous, Christodoulos, Wiltshire, Ron J. (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

On the continuation of solutions for elliptic equations in two variables

Frank Müller (2002)

Annales de l'I.H.P. Analyse non linéaire

On the Dirac delta as initial condition for nonlinear Schrödinger equations

V. Banica, L. Vega (2008)

Annales de l'I.H.P. Analyse non linéaire

On the generalized Maxwell-Bloch equations.

Saksida, Pavle (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

On the mixed problem for hyperbolic partial differential-functional equations of the first order

Tomasz Człapiński (1999)

Czechoslovak Mathematical Journal

We consider the mixed problem for the hyperbolic partial differential-functional equation of the first order $D_{x} z (x, y) = f (x, y, z_{(x, y)}, D_{y} z (x, y)),$ where $z_{(x, y)} [- τ, 0] \times [0, h] \to ℝ$ is a function defined by $z_{(x, y)} (t, s) = z (x + t, y + s)$ , $(t, s) \in [- τ, 0] \times [0, h]$ . Using the method of bicharacteristics and the method of successive approximations for a certain integral-functional system we prove, under suitable assumptions, a theorem of the local existence of generalized solutions of this problem.

On the nodal set of the second eigenfunction of the laplacian in symmetric domains in $R^{N}$

Lucio Damascelli (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We present a simple proof of the fact that if $Ω$ is a bounded domain in $R^{N}$ , $N \geq 2$ , which is convex and symmetric with respect to $k$ orthogonal directions, $1 \leq k \leq N$ , then the nodal sets of the eigenfunctions of the laplacian corresponding to the eigenvalues $λ_{2}, \dots, λ_{k + 1}$ must intersect the boundary. This result was proved by Payne in the case $N = 2$ for the second eigenfunction, and by other authors in the case of convex domains in the plane, again for the second eigenfunction.

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Oddness of least energy nodal solutions on radial domains.

On a Parabolic Symmetry Problem.

On a priori estimates for positive solutions of a semilinear biharmonic equation in a ball

On a quasilinear elliptic equation and a Riemannian metric invariant under Möbius transformations.

On a quasilinear elliptic equation and a Riemannian metric invariant under Möbius transformations. (Summary).

On decomposable Monge-Ampère equations.

On formal theory of differential equations. I.

On formal theory of differential equations. II.

On formal theory of differential equations. III.

On functions, whose lines of steepest descent bend proportionally to level lines

On linearizing systems of diffusion equations.

On the continuation of solutions for elliptic equations in two variables

On the Dirac delta as initial condition for nonlinear Schrödinger equations

On the generalized Maxwell-Bloch equations.

On the mixed problem for hyperbolic partial differential-functional equations of the first order

On the nodal set of the second eigenfunction of the laplacian in symmetric domains in $R^{N}$

On the static and dynamic study of oscillations for some nonlinear hyperbolic systems of conservation laws

On the symmetries of the differential equation governing damped harmonic vibration.

On the symmetry of blowup solutions to a mean field equation

On the uniqueness of the Cauchy problem for partial differential operators with multiple characteristics

Currently displaying 1 – 20 of 26