Improvements on overdetermined problems associated to the $ p $-Laplacian-Reference-Cited by-同舟云学术

Improvements on overdetermined problems associated to the $ p $-Laplacian

Published:2022 Issue:3 Volume:4 Page:1-14
ISSN:2640-3501
Container-title:Mathematics in Engineering
language:
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Author:

Greco Antonio, ,Pisanu Francesco,

Abstract

<abstract><p>This work presents some improvements on related papers that investigate certain overdetermined problems associated to elliptic quasilinear operators. Our model operator is the $ p $-Laplacian. Under suitable structural conditions, and assuming that a solution exists, we show that the domain of the problem is a ball centered at the origin. Furthermore we discuss a convenient form of comparison principle for this kind of problems.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Mathematical Physics,Analysis

Reference17 articles.

1. M. Belloni, B. Kawohl, A direct uniqueness proof for equations involving the $p$-Laplace operator, Manuscripta Math., 109 (2002), 229–231.

2. M. Cuesta, P. Takáč, A strong comparison principle for positive solutions of degenerate elliptic equations, Differ. Integral Equ., 13 (2000), 721–746.

3. L. Damascelli, B. Sciunzi, Harnack inequalities, maximum and comparison principles, and regularity of positive solutions of $m$-Laplace equations, Calc. Var., 25 (2005), 139–159.

4. J. I. Díaz, J. E. Saa, Existence et unicité de solutions positives pour certaines équations elliptiques quasilinéaires, C. R. Acad. Sci. Paris Sér. I Math., 305 (1987), 521–524.

5. D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of second order, 2 Eds., Springer-Verlag, 1998.

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