Results on entire solutions for a degenerate critical elliptic equation with anisotropic coefficients

In this paper, we study the following degenerate critical elliptic equations with anisotropic coefficients $$-div(|x_{N}|^{2\alpha}\nabla u)=K(x)|x_{N}|^{\alpha\cdot 2^{*}(s)-s}|u|^{2^{*}(s)-2}u {in} \mathbb{R}^{N}$$ where $x=(x_{1},...,x_{N})\in\mathbb{R}^{N},$ $N\geq 3,$ $\alpha>1/2,$ $0\leq s\leq 2$ and $2^{*}(s)=2(N-s)/(N-2).$ Some basic properties of the degenerate elliptic operator $-div(|x_{N}|^{2\alpha}\nabla u)$ are investigated and some regularity, symmetry and uniqueness results for entire solutions of this equation are obtained. We also get some variational identities for solutions of this equation. As a consequence, we obtain some nonexistence results for solutions of this equation.Comment: 29 page

The Future of International Investment Regulation: Towards a World Investment Organisation?

With growth in foreign investment and in the number of companies investing in foreign countries, the application of general principles of public international law has not been deemed adequate to regulate foreign investment and there is, as yet, no comprehensive international treaty on the regulation of foreign investment. Consequently, states have resorted to bilateral investment treaties (BITs), regional trade and international investment agreements (IIAs) and free trade agreements (FTAs) to supplement and complement the regime of protection for foreign investors. In the absence of an international investment court, states hosting foreign investment or investor states have opted for investor-state dispute settlement mechanism (ISDS). This mechanism has brought about its own challenges to the international law of foreign investment due to inconsistency in the application and interpretation of the key principles of international investment law by such arbitration tribunals, and further, there is no appellate mechanism to bring about some cohesion and consistency in jurisprudence. Therefore, there are various proposals mooted by scholars to address these challenges and they range from tweaks to BITs and IIAs, the creation of an appellate mechanism and the negotiation of a multilateral treaty to proposals for reform of ISDS only. After assessing the merits and demerits of such proposals, this study goes further, arguing for the creation of a World Investment Organisation (WIO) with a standing mechanism for settlement of investment disputes in order to ensure legal certainty, predictability and the promotion of the flow of foreign investment in a sustainable and responsible manner

HARDY-SOBOLEV-MAZ'YA INEQUALITIES: SYMMETRY AND BREAKING SYMMETRY OF EXTREMAL FUNCTIONS

Denote points in \u211d^k 7R^{N - k} as pairs \u3be = (x,y), and assume 2 64 k < N. In this paper, we study the problem -\u394 v=\u3bb|x|^{-2} v+ |x|{-b}v^{p-1} in \u211d^N, x 60 0, \u3bd > 0 where $p > 2, b = N - pN - 2\2 and \u3bb 64 (k-2\2)2, the Hardy constant. We prove existence, symmetry and breaking symmetry results

HARDY-SOBOLEV-MAZ'YA INEQUALITIES: SYMMETRY AND BREAKING SYMMETRY OF EXTREMAL FUNCTIONS

Denote points in \u211d^k 7R^{N - k} as pairs \u3be = (x,y), and assume 2 64 k < N. In this paper, we study the problem -\u394 v=\u3bb|x|^{-2} v+ |x|{-b}v^{p-1} in \u211d^N, x 60 0, \u3bd > 0 where $p > 2, b = N - pN - 2\2 and \u3bb 64 (k-2\2)2, the Hardy constant. We prove existence, symmetry and breaking symmetry results

On a Sobolev-type inequality related to the weighted p-Laplace operator

In this paper we deal with some Sobolev-type inequalities with weights that were proved by Maz'ya in 1980 and by Caffarelli, Kohn and Nirenberg in 1984. In particular, we deal with the existence of extremals

Provisional Measures in ICSID Arbitration. From \u201cWonderland\u2019s Jurisprudence\u201d to Informal Modification of Treaties

A long stream of substantially identical decisions rendered by ICSID tribunals, starting with Maffezini v. Spain, have upheld their power to order provisional measures under Article 47 ICSID Convention. Since Article 47 ICSID Convention expressly authorizes ICSID tribunals only to recommend such measures, it is worth examining the significance and implications of these decisions from the standpoint of the law of the treaties. The paper first offers a concise discussion of the nature and role of provisional measures in the settlement of international disputes before reviewing the leading cases of the International Court of Justice (ICJ) and other international tribunals (sections II to IV). It then briefly describes the emergence of what appears to be a jurisprudence constante in ICSID investment arbitration (section V) and examines the persuasiveness of the underlying legal reasoning (section VI). Section VII is consecrated to the attitude of ICSID membership with regard to these decisions. The final objective of the paper is to appraise the impact of the concordant body of decisions in combination with the (lack of) reaction of member parties to the ICSID Convention from the standpoint of the interpretation and possibly the informal modification of Article 47