Preheat oven to 350 degrees.
Heat small amount of oil in large skillet. Add celery, red pepper and onion to pan. Cook until soft, not brown. Remove from pan and let cool.
Add crabmeat, dill, mustard and corn flakes to the vegetables.
In separate bowl, beat eggs and then add to crabmeat mixture. Mixture should be moist. If needed, add another egg. Shape the mixture into balls and then flatten.
Heat the remaining oil in skillet over medium heat. Cook crab cakes until golden brown, about 3 minutes on each side. Remove and place on baking sheet. Place in oven and bake for 8-10 minutes.