The best constant in the G-N inequality for the mixed local and nonlocal Laplacian is established, with the optimizer proven to be the ground state solution of the equation.
Nagy, Uber Integralungleichungen zwischen einer Funktion und ihrer Ableitung, Acta Uni- versitatis Szegediensis Sectio Scientiarum Mathematicarum, 10 (1941), 64-74
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The best constant in the G-N inequality for the mixed local and Nonlocal Laplacian
The best constant in the G-N inequality for the mixed local and nonlocal Laplacian is established, with the optimizer proven to be the ground state solution of the equation.