On the Pohozaev identity for quasilinear Finsler anisotropic equations

In this paper we derive the Pohozaev identity for quasilinear equations \begin{equation}\tag{$E$}\label{eq:p} -\operatorname{div}(B’(H(\nabla u))\nabla H(\nabla u))=g(x, u) \quad \text {in},, \Omega, \end{equation} involving the anisotropic Finsler operator $-\operatorname{div}(B’(H(\nabla u))\nabla H(\nabla u))$. In particular, by means of fine regularity results on the vectorial field $B^{\mathrm{\prime }}(H(\mathrm{\nabla }u))\mathrm{\nabla }H(\mathrm{\nabla }u)$, we prove the identity for weak solutions and in a direct way.