SAN FRANCISCO — If U.S. District Judge Lucy Koh has her way, Apple, Samsung and their teams of elite lawyers will spend next week reliving the patent trial of the century.

The parties are reuniting in a San Jose courtroom to make their cases to a jury once more, this time dueling over how much Samsung should have to pay Apple for copying several of its patented features. Koh ordered the retrial in March, finding the original jury’s landmark $1.05 billion award to Apple was tainted by an improper notice date. She has insisted that the new trial must be a virtual replay of the first and barred the parties from introducing new evidence or legal theories.