O ct 2 00 5 NEW MONOTONICITY FORMULAE FOR SEMI - LINEAR ELLIPTIC AND PARABOLIC SYSTEMS
نویسنده
چکیده
where t1 < t2 are two constants, (fi(~u)) is given as above. Our new monotonicity formulae are focused on more attention to the monotonicity of non-linear terms. Our point of view is that we introduce an index called β to measure the monotonicity of the non-linear terms in the problems. The index in the study of monotonicity formulae is very useful in understanding the behavior of blow up sequences of solutions. Corresponding monotonicity results for free boundary problems are also presented.
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