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Abstract
We consider a generalization of the Allen-Cahn type equation in divergence form $-\rm{div}(\nabla G(\nabla u(x,y)))+F_u(x,y,u(x,y))=0$. This is more general than the usual Laplace operator. We prove the existence and regularity of heteroclinic solutions under standard ellipticity and $m$-growth conditions.
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- Copyright (2018 Juliusz Schauder Center for Nonlinear Studies)
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
Topological Methods in Nonlinear Analysis
no. 52,
pages 729 - 738,
ISSN: 1230-3429 - Language:
- English
- Publication year:
- 2018
- Bibliographic description:
- Wroński K.: Heteroclinic solutions of Allen-Cahn type equations with a general elliptic operator// Topological Methods in Nonlinear Analysis. -Vol. 52, nr. 2 (2018), s.729-738
- DOI:
- Digital Object Identifier (open in new tab) 10.12775/tmna.2018.010
- Verified by:
- Gdańsk University of Technology
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