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.
Nash, Continuity of solutions of parabolic and elliptic equations, American Journal of Math- ematics, 80 (1958), 931-954
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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.