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.
Gagliardo, Ulteriori proprieta di alcune classi di funzioni in piu variabili, Ricerche di Matem- atica, 8 (1959), 24-51
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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.