### Heteroclinic solutions of Allen-Cahn type equations with a general elliptic operator

DOI: http://dx.doi.org/10.12775/TMNA.2018.010

#### Abstract

We consider a generalization of the Allen-Cahn type equation in divergence form

$-\rom{div}(\nabla G(\nabla u(x,y)))+F_u(x,y,u(x,y))=0$.

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.

$-\rom{div}(\nabla G(\nabla u(x,y)))+F_u(x,y,u(x,y))=0$.

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.

#### Keywords

Heteroclinic solutions; Allen-Cahn equation

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