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$C^{1}$ -regularity of the Aronsson equation in $R^{2}$

Changyou Wang, Yifeng Yu (2008)

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

$C^{1, α}$ convergence of minimizers of a Ginzburg-Landau functional.

Lei, Yutian, Wu, Zhuoqun (2000)

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

$C^{1, α}$ local regularity for the solutions of the $p$ -Laplacian on the Heisenberg group. The case $1 + \frac{1}{\sqrt{5}} < p \leq 2$

Silvana Marchi (2003)

Commentationes Mathematicae Universitatis Carolinae

We prove the Hölder continuity of the homogeneous gradient of the weak solutions $u \in W_{loc}^{1, p}$ of the p-Laplacian on the Heisenberg group $ℋ^{n}$ , for $1 + \frac{1}{\sqrt{5}} < p \leq 2$ .

$C^{1, α}$ regularity for elliptic equations with the general nonstandard growth conditions

Sungchol Kim, Dukman Ri (2024)

Mathematica Bohemica

We study elliptic equations with the general nonstandard growth conditions involving Lebesgue measurable functions on $Ω$ . We prove the global $C^{1, α}$ regularity of bounded weak solutions of these equations with the Dirichlet boundary condition. Our results generalize the $C^{1, α}$ regularity results for the elliptic equations in divergence form not only in the variable exponent case but also in the constant exponent case.

$C^{\infty}$ interfaces of solutions for one-dimensional parabolic $p$ -Laplacian equations.

Ham, Yoonmi, Ko, Youngsang (1999)

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

$C^{k}$ -estimates for the Cauchy-Riemann equations on certain weakly pseudoconvex domains

Jerzy Ryczaj (1987)

Colloquium Mathematicae

$C^{k}$ -regularity for the $\bar{\partial}$ -equation on a piecewise smooth union of strictly pseudoconvex domains in $ℂ^{n}$

Joachim Michel, Alessandro Perotti (1994)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

$C^{\infty}$ regularity of solutions of a quasilinear equation related to the Levi operator

G. Citti (1996)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

$C^{\infty}$ regularity of solutions of the Levi equation

G. Citti (1998)

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

$C^{\infty}$ -well posedness of the Cauchy problem for quasi-linear hyperbolic equations with coefficients non-Lipschitz in time and smooth in space

Akisato Kubo, Michael Reissig (2003)

Banach Center Publications

In this paper we prove the $C^{\infty}$ -well posedness of the Cauchy problem for quasi-linear hyperbolic equations of second order with coefficients non-Lipschitz in t ∈ [0,T] and smooth in x ∈ ℝⁿ.

$C^{α}$ -regularity results for quasilinear parabolic systems

Alain Bensoussan, Jens Frehse (1990)

Commentationes Mathematicae Universitatis Carolinae

C2-Regularity for Partially Free Minimal Surfaces.

Gerhard Dziuk (1985)

Mathematische Zeitschrift

Caccioppoli estimates and very weak solutions of elliptic equations

Tadeusz Iwaniec, Carlo Sbordone (2003)

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

Caccioppoli estimates are instrumental in virtually all analytic aspects of the theory of partial differential equations, linear and nonlinear. And there is always something new to add to these estimates. We emphasize the fundamental role of the natural domain of definition of a given differential operator and the associated weak solutions. However, we depart from this usual setting (energy estimates) and move into the realm of the so-called very weak solutions where important new applications lie....

Cahn-Hilliard equation with terms of lower order and non-constant mobility.

Changchun, Liu (2003)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Calcul de la solution élémentaire de l'opérateur d'Euler-Poisson-Darboux et de l'opérateur de Tricomi-Clairaut, hyperbolique, d'ordre 2

S. Delache, J. Leray (1971)

Bulletin de la Société Mathématique de France

Calcul de Weyl et opérateurs sous elliptiques

C. E. Cancelier, J. Y. Chemin, C. J. Xu (1993)

Annales de l'institut Fourier

Calcul de Weyl et opérateurs sous-elliptiques

C. E. Cancelier, J.-Y. Chemin, C. J. Xu (1991/1992)

Séminaire Équations aux dérivées partielles (Polytechnique)

Calcul des courants induits et des forces électromagnétiques dans un système de conducteurs mobiles

A. Bossavit (1989)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Calcul des singularités par la méthode des éléments finis

P. Laurent-Gengoux, D. Neveu (1990)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. II

Takashi Aoki (1986)

Annales de l'institut Fourier

Soit $P$ un opérateur pseudodifférentiel (ou microdifférentiel) tel que $exp P$ soit aussi un opérateur pseudodifférentiel. Alors le symbole de $exp P$ s’ecrit $exp q$ avec un symbole $q$ . Pour la réciproque, si $Q$ est un opérateur à symbole $exp q$ , il existe un opérateur $P$ tel que $Q = exp P$ . Tous ces résultats reposent sur la théorie développée dans la Note I de cette série. Comme application, on obtient une condition suffisante d’inversibilité pour les opérateurs pseudodifférentiels d’ordre infini.

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