A. This structure, near La Guardia Place, requires far more delicate techniques of research than the typical New York building, including collating information from tax records, deeds, directories and building permits.
Mechanical excavators, airlifts and suction dredges were used in the process of locating the wreck, but as soon as it began to be uncovered in earnest, more delicate techniques were employed.
A newer, more delicate technique is known as knock-in technology.
The loss of (AR) condition renders variational techniques more delicate.
The lack of compactness of the Sobolev embedding makes standard variational techniques more delicate.
Under the assumption (V1), the compactness of the embedding is lost and this renders variational techniques more delicate.
In this present work, as the domain is unbounded, the lack of compactness of the Sobolev embedding (W_{0}^{1,p}(Omega)hookrightarrow L^{q}(Omega)) ((pleq q < p^:=frac{pN}{N-p} )) makes standard variational techniques more delicate.
Note that although the idea was earlier used for other problems, the adaptation to the procedure to our problem is not trivial at all since the parameters (r,m) satisfy (1< r< m) and we must consider our problem for a suitable space, and so we need more delicate estimates and new technique.
We remark that some ideas of our methods are taken from [4, 21], but our methods and technique are more delicate and complex than those used in [4, 15, 21].
After recalling some notation and establishing some preliminary lemmas, we will prove Theorem 1.1 in Section 2. And the proof of Theorem 1.2 will be given in Section 3. We remark that our some ideas in the proofs of our main results are taken from [3, 9, 11, 17], but our methods and technique are more delicate and complex than those used in [3, 9, 11, 17].
Johan showed extreme patience during the first few months as I tried to learn the experimental techniques that were much more delicate than ones I used previously.
