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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 $1 + \frac{1}{\sqrt{5}} < p \leq 2$ .

$C^{\infty}$ 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

Caractère lipschitzien d'une distance associée à des champs de vecteurs engendrant une algèbre de Lie de rang maximal. Quelques conséquences

Rose-Marie Hervé, Michel Hervé (1990)

Annales de l'institut Fourier

La métrique attachée de façon naturelle à des champs de vecteurs $C^{\infty}$ est susceptible de plusieurs définitions voisines ; on montre que, suivant la définition adoptée, elle peut avoir, ou ne pas avoir, un caractère localement lipschitzien qui a pour conséquence l’existence de points $L$ -réguliers, pour certains opérateurs différentiels $L$ , sur les frontières des boules pour la métrique.

Carleman estimates for a subelliptic operator and unique continuation

Nicola Garofalo, Zhongwei Shen (1994)

Annales de l'institut Fourier

We establish a Carleman type inequality for the subelliptic operator $ℒ = Δ_{z} + | x |^{2} \partial_{t}^{2}$ in $ℝ^{n + 1}$ , $n \geq 2$ , where $z \in ℝ^{n}$ , $t \in ℝ$ . As a consequence, we show that $- ℒ + V$ has the strong unique continuation property at points of the degeneracy manifold ${(0, t) \in ℝ^{n + 1} | t \in ℝ}$ if the potential $V$ is locally in certain $L^{p}$ spaces.

Classical, viscosity and average solutions for PDE’s with nonnegative characteristic form

Cristian E. Gutiérrez, Ermanno Lanconelli (2004)

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

We compare several definitions of weak solutions to second order partial differential equations with nonnegative characteristic form.

Compact imbeddings in weighted Sobolev spaces and nonlinear boundary value problems

Pavel Drábek, Alois Kufner (1994)

Acta Mathematica et Informatica Universitatis Ostraviensis

Compacteness methods for certain degenerate elliptic systems.

Lihe Wang (1993)

Manuscripta mathematica

Comparison results for semilinear elliptic equations via Picone-type identities.

Tadie (2009)

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

Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results

Lucio Damascelli (1998)

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

Comportement asymptotique des valeurs propres d'une classe d'opérateurs elliptiques et dégénérés en dimension 2

Pham The Lai (1974)

Journées équations aux dérivées partielles

Comportement asymptotique des valeurs propres d’une classe d’opérateurs elliptiques dégénérés en dimension $2$

The Lai Pham (1974)

Publications mathématiques et informatique de Rennes

Comportement asymptotique des valeurs propres pour une classe d'opérateurs elliptiques dégénérés

Monique Sable-Tougeron (1978)

Publications mathématiques et informatique de Rennes

Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems

Shigeru Sakaguchi (1987)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Concentration-compactness principle for variable exponent spaces and applications.

Bonder, Julián Fernández, Silva, Analía (2010)

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

Constant sign and nodal solutions for problems with the $p$ -Laplacian and a nonsmooth potential using variational techniques.

Agarwal, Ravi P., Filippakis, Michael E., O'Regan, Donal, Papageorgiou, Nikolaos S. (2009)

Boundary Value Problems [electronic only]

Construction of a Singular Elliptic-Harmonic Measure.

L. Modica, St. Mortola (1980/1981)

Manuscripta mathematica

Continuity, curvature, and the general covariance of optimal transportation

Young-Heon Kim, Robert McCann (2010)

Journal of the European Mathematical Society

Continuity of solutions of linear, degenerate elliptic equations

Jani Onninen, Xiao Zhong (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We consider the simplest form of a second order, linear, degenerate, elliptic equation with divergence structure in the plane. Under an integrability condition on the degenerate function, we prove that the solutions are continuous.

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