Volume 35, Issue 1
Rigidity of Minimizers in Nonlocal Phase Transitions II

Anal. Theory Appl., 35 (2019), pp. 1-27.

Published online: 2019-04

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• Abstract

In this paper we extend the results of [12] to the borderline case $s = \frac 12$. We obtain the classification of global bounded solutions with asymptotically flat level sets for semilinear nonlocal equations of the type $$\Delta ^{\frac 12} u=W'(u) \quad \mbox{in}\quad \ R^n,$$where $W$ is a double well potential.

• Keywords

De Giorgi’s conjecture, fractional Laplacian.

• AMS Subject Headings

35J61

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COPYRIGHT: © Global Science Press

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@Article{ATA-35-1, author = {}, title = {Rigidity of Minimizers in Nonlocal Phase Transitions II}, journal = {Analysis in Theory and Applications}, year = {2019}, volume = {35}, number = {1}, pages = {1--27}, abstract = {

In this paper we extend the results of [12] to the borderline case $s = \frac 12$. We obtain the classification of global bounded solutions with asymptotically flat level sets for semilinear nonlocal equations of the type $$\Delta ^{\frac 12} u=W'(u) \quad \mbox{in}\quad \ R^n,$$where $W$ is a double well potential.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-0008}, url = {http://global-sci.org/intro/article_detail/ata/13090.html} }
TY - JOUR T1 - Rigidity of Minimizers in Nonlocal Phase Transitions II JO - Analysis in Theory and Applications VL - 1 SP - 1 EP - 27 PY - 2019 DA - 2019/04 SN - 35 DO - http://dor.org/10.4208/ata.OA-0008 UR - https://global-sci.org/intro/ata/13090.html KW - De Giorgi’s conjecture, fractional Laplacian. AB -

In this paper we extend the results of [12] to the borderline case $s = \frac 12$. We obtain the classification of global bounded solutions with asymptotically flat level sets for semilinear nonlocal equations of the type $$\Delta ^{\frac 12} u=W'(u) \quad \mbox{in}\quad \ R^n,$$where $W$ is a double well potential.

O. Savin. (2020). Rigidity of Minimizers in Nonlocal Phase Transitions II. Analysis in Theory and Applications. 35 (1). 1-27. doi:10.4208/ata.OA-0008
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