Bojarski–Meyers Inequality for Solutions of a p-Elliptic Equation with Lower-Order Terms and the Zaremba Boundary Condition. The Critical Case

Key Points

• This research aims to establish the existence of solutions and energy bounds for a specific class of p-elliptic equations with lower-order terms.
• Proved the existence of solutions to the p-elliptic equation.
• Demonstrated energy bounds for solutions.
• Analyzed summability of the solution's gradient in a Lipschitz domain.
• Established existence of a solution under the Zaremba boundary condition.
• Showed improved gradient summability for solutions in bounded domains.
• Confirmed energy bounds which constrain solution behavior.