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Deep learning methods can struggle to handle domain shifts not seen in training data, which can cause them to not generalize well to unseen domains. This has led to research attention on domain generalization (DG), which aims to the model's generalization ability to out-of-distribution. Adversarial domain generalization is a popular approach to DG, but conventional approaches (1) struggle to sufficiently align features so that local neighborhoods are mixed across domains; and (2) can suffer from feature space over collapse which can threaten generalization performance. To address these limitations, we propose localized adversarial domain generalization with space compactness maintenance~(LADG) which constitutes two major contributions. First, we propose an adversarial localized classifier as the domain discriminator, along with a principled primary branch. This constructs a min-max game whereby the aim of the featurizer is to produce locally mixed domains. Second, we propose to use a coding-rate loss to alleviate feature space over collapse. We conduct comprehensive experiments on the Wilds DG benchmark to validate our approach, where LADG outperforms leading competitors on most datasets.