A comparison theorem for the Levi equation

Giovanna Citti

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993)

  • Volume: 4, Issue: 3, page 207-212
  • ISSN: 1120-6330

Abstract

top
We prove a strong comparison principle for the solution of the Levi equation L ( u ) = ∑ i = 1 n ( ( 1 + u t 2 ) ( u x i ⁢ x i + u y i ⁢ y i ) + ( u x i 2 + u y i 2 ) u t ⁢ t + 2 ( u y i - u x i u t ) u x i ⁢ t - 2 ( u x i + u y i u t ) u y i ⁢ t + k ( x , y , t ) ( 1 + | D u | 2 ) 3 / 2 = 0 , applying Bony Propagation Principle.

How to cite

top

Citti, Giovanna. "A comparison theorem for the Levi equation." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 4.3 (1993): 207-212. <http://eudml.org/doc/244129>.

@article{Citti1993,
abstract = {We prove a strong comparison principle for the solution of the Levi equation \( L(u) = \sum\_\{i=1\}^\{n\} ((1 + u\_\{t\}^\{2\}) (u\_\{x\_\{i\}x\_\{i\}\} + u\_\{y\_\{i\}y\_\{i\}\} ) + (u\_\{x\_\{i\}\}^\{2\} + u\_\{y\_\{i\}\}^\{2\}) u\_\{tt\} + 2(u\_\{y\_\{i\}\} - u\_\{x\_\{i\}\} u\_\{t\}) u\_\{x\_\{i\}t\} - 2(u\_\{x\_\{i\}\} + u\_\{y\_\{i\}\} u\_\{t\}) u\_\{y\_\{i\}t\} + k (x,y,t) (1 + |Du|^\{2\})^\{3/2\} = 0 \), applying Bony Propagation Principle.},
author = {Citti, Giovanna},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Maximum propagation principle; Comparison principle; Levi equation; strong comparison principle; Bony propagation principle},
language = {eng},
month = {9},
number = {3},
pages = {207-212},
publisher = {Accademia Nazionale dei Lincei},
title = {A comparison theorem for the Levi equation},
url = {http://eudml.org/doc/244129},
volume = {4},
year = {1993},
}

TY - JOUR
AU - Citti, Giovanna
TI - A comparison theorem for the Levi equation
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1993/9//
PB - Accademia Nazionale dei Lincei
VL - 4
IS - 3
SP - 207
EP - 212
AB - We prove a strong comparison principle for the solution of the Levi equation \( L(u) = \sum_{i=1}^{n} ((1 + u_{t}^{2}) (u_{x_{i}x_{i}} + u_{y_{i}y_{i}} ) + (u_{x_{i}}^{2} + u_{y_{i}}^{2}) u_{tt} + 2(u_{y_{i}} - u_{x_{i}} u_{t}) u_{x_{i}t} - 2(u_{x_{i}} + u_{y_{i}} u_{t}) u_{y_{i}t} + k (x,y,t) (1 + |Du|^{2})^{3/2} = 0 \), applying Bony Propagation Principle.
LA - eng
KW - Maximum propagation principle; Comparison principle; Levi equation; strong comparison principle; Bony propagation principle
UR - http://eudml.org/doc/244129
ER -

References

top
  1. BONY, J. M., Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés. Ann. Inst. Fourier (Grenoble), 19, 1969, 277-304. Zbl0176.09703MR262881
  2. BEDFORD, E. - GAVEAU, B., Hypersurfaces with bounded Levi form. Ind. Univ. Mat. J., 27, no. 5, 1978, 867-873. Zbl0365.32011MR499287
  3. DEBIARD, A. - GAVEAU, B., Problème de Dirichlet pour l'équation de Levi. Bull. Sc. Math., II, 102, no. 4, 1978, 369-386. Zbl0411.35015MR517769
  4. TOMASSINI, G., Geometric properties of solutions of the Levi equation. Ann. di Mat. Pura e Appl., 152, 1988, 331-344. Zbl0681.35017MR980986DOI10.1007/BF01766155
  5. TOMASSINI, G., Nonlinear equations related to the Levi form. Rend. Circ. Mat. Palermo, Ser. II, T. XL, 1991, 281-297. Zbl0836.35056MR1151589DOI10.1007/BF02844692

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.