On a class of anisotropic nonlinear elliptic equations with variable exponent (Q362752)

Summary: Based on truncation technique and a priori estimates, we prove the existence and uniqueness of weak solutions for a class of anisotropic nonlinear elliptic equations with variable exponent \(\vec{p(x)}\) growth. Furthermore, we also obtain that the weak solution is locally bounded and regular; that is, the weak solution is \(L^\infty_{\text{loc}}(\Omega)\) and \(C^{1, \alpha}(\Omega)\).