The world's two biggest makers of smartphones — U.S.-based Apple and South Korea's Samsung Electronics — are squaring off in a U.S. court over competing patent rights claims for the lucrative devices.

Billions of dollars are at stake in the dispute that will be decided by a jury in California, not far from Apple's headquarters. The case, starting Monday with jury selection, is expected to last several weeks. It is one of several being contested by the two technology giants in courts on four continents around the world.

Dominance in the $312 billion mobile technology industry is at stake. In the April-to-June period alone this year, consumers bought more than 400 million mobile devices. Samsung shipped more than 50 million of the popular products, nearly twice as many as Apple.

Apple claims that Samsung copied designs of its popular iPhone and iPad devices and used them to create its own line of Galaxy devices. Apple is demanding $2.5 billion in damages for what it claims are patent infringements.

Samsung contends it has proof that by 2006 — months before Apple introduced its first iPhone in early 2007 — it was developing a next generation of smartphones with a rounded rectangular body that both companies now use.

The judge presiding over the case, Lucy Koh, ordered the chief executives from the firms — Apple's Tim Cook and Samsung's Choi Gee Sung — to meet to try work out a settlement of the dispute. They met in May but were unable to reach an agreement.