Abstract: Using the regularizing effect between the coefficient of the zero order term and the righthand side term of the equation, the author considered a class of elliptic equations with degenerate coercivity and lower order terms. When the righthand side term f of the equation was only in L¹, the author obtained a priori L^∞ estimate of its weak solution and proved the existence of its weak solutions.

Key words: elliptic equation, degenerate coercivity, righthand side term in L¹