An arrangement and a method for a combustion engine for self-ignition of a fuel mixture. A first device supplies a first partial quantity of the fuel mixture to the combustion space, and a second device supplies a second partial quantity of the fuel mixture to the combustion space, which second partial quantity of the fuel mixture is at a different fuel concentration from the first partial quantity of the fuel mixture. The devices supply the first and the second partial quantities of the fuel mixture as to create in the combustion space at least one region which is at a higher fuel concentration than other regions and in which the self-ignition of the fuel mixture is intended to start.