Radio maps (RMs) provide a spatially continuous description of wireless propagation, enabling cross-layer optimization and unifying communication and sensing for integrated sensing and communications (ISAC). However, constructing high-fidelity RMs at operational scales is difficult, since physics-based solvers are time-consuming and require precise scene models, while learning methods degrade under incomplete priors and sparse measurements, often smoothing away critical discontinuities. We present RMSup, a physics-informed super-resolution framework that functions with uniform sparse sampling and imperfect environment priors. RMSup extracts Helmholtz equation-informed boundary and singularity prompts from the measurements, fuses them with base-station side information and coarse scene descriptors as conditional inputs, and employs a boundary-aware dual-head network to reconstruct a high-fidelity RM and recover environmental contours jointly. Experimental results show the proposed RMsup achieves state-of-the-art performance both in RM construction and ISAC-related environment sensing.