Albert Barnes Commentary Obadiah 1:19

"And they of the South shall possess the mount of Esau, and they of the lowland the Philistines; and they shall possess the field of Ephraim, and the field of Samaria; and Benjamin [shall possess] Gilead." — Obadiah 1:19 (ASV)

And those of the South shall possess the mountain of Esau - The Church was now hemmed in within Judah and Benjamin. They too were to go into captivity. The prophet looks beyond the captivity and the return, and tells how that original promise to Jacob (Genesis 28:14) should be fulfilled: Your seed shall be as the dust of the earth, and you shall break North to the West, and to the East, and to the North, and to the South; and in you and in your seed shall all the families of the earth be blessed. Hosea and Amos had, at this time, prophesied the final destruction of the kingdom of Israel.

Obadiah describes Judah, as expanded to its former boundaries, including Edom and Philistia, and occupying the territory of the ten tribes. The South, that is, those of the hot and dry country to the south of Judah bordering on Edom, shall possess the mountains of Esau, that is, his mountain country, on which they bordered. And the plain, those on the west, in the great maritime plain, the shephelah, shall spread over the country of the Philistines, so that the sea shall be their boundary; and on the north, over the country of the ten tribes, the fields of Ephraim and the fields of Samaria. The territory of Benjamin being thus included in Judah, to Benjamin is assigned the country on the other side of the Jordan: and Benjamin, Gilead.