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.
Citation
Karol Wroński. "Heteroclinic solutions of Allen-Cahn type equations with a general elliptic operator." Topol. Methods Nonlinear Anal. 52 (2) 729 - 738, 2018. https://doi.org/10.12775/TMNA.2018.010