A320
Aircraft Equipment Problem Less Severe
Flight Crew Overcame Equipment Problem; Flight Crew Landed in Emergency Condition
Aircraft
Climbing out at FL190 ECAM alerted us to the fact that our green hydraulic system had low volume; followed by low pressure.  We followed SOP.  Completed QRH and ECAM procedures.  Contacted dispatch with issue who contacted [maintenance].  All agreed to proceed to [destination].  All degraded systems involved landing and taxiing the aircraft.  Took vector to 20 mile final. Completed all QRH; ECAM; and normal ops check lists configured and landed.  Cleared runway on high speed taxiway; with differential braking stopped aircraft and was towed to [gate].Leak in green hydraulic system.
An A320 Captain reported loss of green hydraulic system during the climbout. The Flight continued to the destination.