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Trudinger-Moser inequality is a substitute to the (forbidden) critical Sobolev embedding, namely the case where the scaling corresponds to $L^{\infty}$ . It is well known that the original form of the inequality with the sharp exponent (proved by Moser) fails on the whole plane, but a few modied versions are available. We prove a precised version of the latter, giving necessary and sufficient conditions for the boundedness, as well as for the compactness, in terms of the growth and decay of the nonlinear function....

Two-dimensional source potentials in a two-fluid medium for the modified Helmholtz equation.

Mandal, B.N., Chakrabarti, R.N. (1986)

International Journal of Mathematics and Mathematical Sciences

Two-scale convergence of a model for flow in a partially fissured medium.

Clark, G.W., Showalter, R.E. (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Tykhonov well-posedness of a heat transfer problem with unilateral constraints

Mircea Sofonea, Domingo A. Tarzia (2022)

Applications of Mathematics

We consider an elliptic boundary value problem with unilateral constraints and subdifferential boundary conditions. The problem describes the heat transfer in a domain $D \subset ℝ^{d}$ and its weak formulation is in the form of a hemivariational inequality for the temperature field, denoted by $𝒫$ . We associate to Problem $𝒫$ an optimal control problem, denoted by $𝒬$ . Then, using appropriate Tykhonov triples, governed by a nonlinear operator $G$ and a convex $\tilde{K}$ , we provide results concerning the well-posedness of problems...

Ueber Complexe, insbesondere Linien- und Kugelcomplexe, mit Anwendung auf die Theorie partieller Differential-Gleichungen

Lie (1872)

Mathematische Annalen

Ueber die Lie'schen Berührungs- Transformationen

A. Mayer (1874)

Nachrichten von der Königl. Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen

Ueber unbeschränkt integrable Systeme von linearen totalen Differentialgleichungen und die simultane Integration linearer partieller Differentialgleichungen

Mayer (1872)

Mathematische Annalen

Un invariant algébrique associé à une application continue

Weishu Shih (1986)

Diagrammes

Un théorème de prolongement pour l'opérateur « divergence »

P. Bolley, J. Camus (1976)

Publications mathématiques et informatique de Rennes

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Transformation de Fourier géométrique et microlocalisation

Transformation de Kelvin et ondes non linéaires globales

Transformations de Laplace sur des sous-variétés de $C^{n}$ et représentations d’ondes entrantes et sortantes

Transformations of differential equations

Traveling wave solutions of the heat flow of director fields

Travelling wave solutions for the KdV-Burgers-Kuramoto and nonlinear Schrödinger equations which describe pseudospherical surfaces.

Triangulation formelle de certains systèmes de Pfaff complètement intégrables et application à l’étude $C^{\infty}$ des systèmes non linéaires

Trudinger–Moser inequality on the whole plane with the exact growth condition

Two-dimensional source potentials in a two-fluid medium for the modified Helmholtz equation.

Two-scale convergence of a model for flow in a partially fissured medium.

Tykhonov well-posedness of a heat transfer problem with unilateral constraints

Tzitzeica theory -- opportunity for reflection in mathematics.

Über die Menge erster Integrale gewisser partieller Differetialgleichungen erster Ordnung

Über eine nichtlineare partielle Diferentialgleleichung II ordnung in der nichtanalytische funktionen Erssheinen

Über lineare partielle Differentialgleichungen zweiter Ordnung mit Fundamentalsystemen.