A liquid rocket engine with regeneratively cooled chamber walls and nozzles would definitely be one among those components experiencing the steepest thermal gradients (Chamber wall inner - $3000 K$ and the outer wall - $800 K$, within few millimetres).
How are the engines designed to withstand such significant temperature gradient without failure due to differential expansion? Is the effect simply minuscule considering the size of the engine? Wouldn't the extreme temperature lead to a significant expansion of the inner walls compared to the outer ones?