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We provide a higher integrability result for the gradient of positivesolutions to Trudinger's equation (also known as the doubly non-linearequation) for the range $p\in [2,\infty)$. The estimate is achieved by refininga construction of intrinsic cylinders from the vectorial setting byincorporating estimates only available in the scalar case.

A reverse H\"older inequality for the gradient of solutions to Trudinger's equation