<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we are going to investigate a free boundary value problem for the anisotropic <italic>N</italic>-Laplace operator on a ring domain <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_auom-2020-0027_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mi>Ω</mi><mo>:</mo><mo>=</mo><msub><mrow><mi>Ω</mi></mrow><mn>0</mn></msub><mo>\</mo><msub><mrow><mover><mi>Ω</mi><mo>¯</mo></mover></mrow><mn>1</mn></msub><mo>⊂</mo><msup><mrow><mi>𝕉</mi></mrow><mi>N</mi></msup></mrow></math><tex-math>\Omega : = {\Omega _0}\backslash {\bar \Omega _1} \subset {\mathbb{R}^N}</tex-math></alternatives></inline-formula>, <italic>N</italic> ≥ 2. Our aim is to show that if the problem admits a solution in a suitable weak sense, then the underlying domain Ω is a Wulff shaped ring. The proof makes use of a maximum principle for an appropriate P-function, in the sense of L.E. Payne and some geometric arguments involving the anisotropic mean curvature of the free boundary.</p></abstract>

In this paper we are going to investigate a free boundary value problem for the anisotropic N-Laplace operator on a ring domain Ω:=Ω0\Ω¯1⊂𝕉N\Omega : = {\Omega _0}\backslash {\bar \Omega _1} \subset {\mathbb{R}^N}, N ≥ 2. Our aim is to show that if the problem admits a solution in a suitable weak sense, then the underlying domain Ω is a Wulff shaped ring. The proof makes use of a maximum principle for an appropriate P-function, in the sense of L.E. Payne and some geometric arguments involving the anisotropic mean curvature of the free boundary.

On a free boundary value problem for the anisotropic <italic>N</italic>-Laplace operator on an <italic>N</italic>−dimensional ring domain

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On a free boundary value problem for the anisotropic -Laplace operator on an −dimensional ring domain

In this paper we are going to investigate a free boundary value problem for the anisotropic N-Laplace operator on a ring domain Ω:=Ω0\Ω¯1⊂𝕉N\Omega : = {\Omega...

On a free boundary value problem for the anisotropic N-Laplace operator on an N−dimensional ring domain

Published Online: Sep 22, 2020

Page range: 195 - 208

Received: Oct 13, 2019

Accepted: Dec 15, 2019

DOI: https://doi.org/10.2478/auom-2020-0027

Keywords
Anisotropic equations, maximum principles, overdetermined problems, radially symmetry

© 2020 A. E. Nicolescu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On a free boundary value problem for the anisotropic N-Laplace operator on an N−dimensional ring domain

Published Online: Sep 22, 2020

Page range: 195 - 208

Received: Oct 13, 2019

Accepted: Dec 15, 2019

DOI: https://doi.org/10.2478/auom-2020-0027

KeywordsAnisotropic equations, maximum principles, overdetermined problems, radially symmetry

© 2020 A. E. Nicolescu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Anisotropic equations, maximum principles, overdetermined problems, radially symmetry