If Laplace equation satisfies, then which of the following statements will be true?

If the Laplace equation is satisfied, it generally means that the following statements are true:

1. The function is harmonic: The solution to the Laplace equation is a harmonic function, which implies that it averages to zero over the surface of any sphere. This means that, within a given domain, the value of the function at any point is the average of its values over any sphere centered at that point.

2. The function represents a steady-state heat distribution in the absence of sources or sinks: In the context of heat transfer, a solution to the Laplace equation represents a temperature distribution that does not change over time (steady state) in a domain without any internal heat sources (like heaters) or sinks (cooling elements).

3. The function is analytic everywhere within its domain: The solutions to the Laplace equation are smooth and differentiable at all points within the domain where the equation is satisfied. This implies that these functions can be represented by a convergent power series (Taylor series) within this domain, characterizing them as analytic functions.

4. There are no local maxima or minima within the domain: According to the maximum principle for harmonic functions, any local extremum of a solution to the Laplace equation in a domain must occur on the boundary of that domain. This means that, within the domain, the function cannot have a value higher or lower than any value it takes on the boundary.

5. **The solution is uniquely determined if boundary conditions