After graduating from high school in 1925, Sobolev entered the Physics and Mathematics Faculty of Leningrad State University where his talents were quickly spotted by Smirnov who had returned to Leningrad three years earlier. Sobolev became interested in differential equations, a topic which would dominate his research throughout his life, and even at this stage in his career he produced new results which he published.
Pagkatapos graduating mula sa mataas na paaralan sa 1925, Sobolev ipinasok ang Physics at Mathematics Faculty ng Leningrad State University na kung saan ang kanyang mga talento ay mabilis na batik-batik sa pamamagitan ng Smirnov na ibabalik sa Leningrad tatlong taon na mas maaga. Sobolev naging interesado sa mga kaugalian equation, ng isang paksa kung saan ay mangibabaw ang kanyang mga pananaliksik sa kabuuan ng kanyang buhay, at kahit na sa hakbang na ito sa kanyang karera siya ginawa ng bagong mga resulta na nai-publish na siya.