Consider the equation

usually we call the equation is subcritical when , supercritical when . The reason comes from the scalling the solution. Suppose is a solution of the equation, then is another solution. Consider the energy possessed by around any point of radius can be bounded

when , we scale to , then will become in order to be a solution and lives on . While the energy will be

If the , which is , the energy bound of will become . Since , the bound deteriorates by ‘zooming in’. In this case, we call the equation is supercritical. The solution looks more singular at this time.

**Remark:** The energy should include , but somehow this term scale differently with and can not give one the critical exponent exactly.

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