Jamieson, Fausset and Brown on Isaiah 11:4

4. judge--see that impartial justice is done them. "Judge" may mean here "rule," as in Psa 67:4.

reprove--or, "argue"; "decide." But Lowth, "work conviction in."

earth--Compare with Mt 5:5, and Re 11:15.

earth--its ungodly inhabitants, answering to "the wicked" in the parallel, and in antithesis to the "poor" and "meek," namely, in spirit, the humble pious (Mt 5:3). It is at the same time implied that "the earth" will be extraordinarily wicked when He shall come to judge and reign. His reign shall therefore be ushered in with judgments on the apostates (Psa 2:9-12; Lu 18:8; Re 2:27).

rod of ... mouth--condemning sentences which proceed from His mouth against the wicked (Re 1:16; 2:16; 19:15, 21).

breath of ... lips--his judicial decisions (Is 30:28; Job 15:30; Re 19:20; 20:9-12). He as the Word of God (Re 19:13-15) comes to strike that blow which shall decide His claim to the kingdom, previously usurped by Satan, and "the beast" to whom Satan delegates his power. It will be a day of judgment to the Gentile dispensation, as the first coming was to the Jews. Compare a type of the "rod" (Nu 17:2-10).