The terminology "very weak" is used to emphasize the fact that such solutions do not belong, in general, to the natural Sobolev space W 1, p , i.e. they are not energy solutions.
For p>p∗ we construct a nonlinearity f x,s)="a(x)sp together with a positive very weak solution which does not belong to L∞. Finally we exhibit a class of domains for which p*= p*.
In this paper it is established that in an infinite angular domain for Dirichlet problem of the heat conduction equation the unique (up to a constant factor) non-trivial solution exists, which does not belong to the class of summable functions with the found weight.
In an infinite angular domain for the homogeneous Dirichlet problem for the heat conduction equation the existence of a unique (up to a constant factor) non-trivial solution, which, however, does not belong to the class of summable functions with the weight found in the work is proved.
Therefore, if (alpha< 1) and the condition (52) is not satisfied, the solution of Problem D2 does not belong to (C^{2}(Q_{0}) cap C ( overline{Q} ) ) in general.
Therefore, there exists at least one Pareto-optimal solution, say x*, that does not belong to the union set ΩU2, which means, according to the definition of ΩU2 in Eq. 12, we have ( g_{i} (x_{i} ) < g_{i} (x*) ) for all i = 1, ···, N Obj.
Finally, some results for internal flows with embedded shocks are presented, including a case for which the solution to the inverse problem does not belong to the design space.
But x does not belong to the solution set of (LVQEPLEC).
In general, does not belong to But we can see easily from that a solution of (1.3) must belong to.
The soldier does not belong.
