No read on villain.

PokerStars No-Limit Hold'em, $0.05 BB (7 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

MP2 ($9.97)
CO ($6)
Button ($1.78)
Hero ($4.98)
BB ($3.46)
UTG ($1.98)
MP1 ($13.45)

Preflop: Hero is SB with K, K. CO posts a blind of $0.05.
UTG calls $0.05, 2 folds, CO (poster) checks, Button calls $0.05, Hero raises to $0.45, 1 fold, UTG folds, CO folds, Button calls $0.40.

Flop: ($1.07) A, J, 8 (2 players)
Hero hates this spot, sighs and ???

Does my hand still have value against his range which contains a lot of Ax hands?