the eczema could be an allergic reaction so if you are bottle feeding ask your doctor for a cow's milk and/or soy free formula or if you are breast feeding you could try avoiding allergic foods such cow's milk, soy, eggs, peanuts and wheat for a couple of weeks and see if is any change. Also cleaning the affected area with breast milk once or twice per day could help and if not, it wont do any harm since breast milk will help keep the moisture.
If it doesn't help i would consult my pediatrician or a homeopath (if you are looking for more natural alternatives) before applying anything else since every baby's skin is different and very easy to irritate.
Best luck,
Carolina