Optimal higher-order Sobolev type embeddings are shown to follow via isoperimetric inequalities. This establishes a higher-order analogue of a well-known link between first-order Sobolev embeddings and isoperimetric inequalities. Sobolev type inequalities of any order, involving arbitrary rearrangement-invariant norms, on open sets in R n , possibly endowed with a measure density, are reduced to much simpler one-dimensional inequalities for suitable integral operators depending on the isoperimetric function of the relevant sets. As a consequence, the optimal target space in the relevant Sobolev embeddings can be determined both in standard and in non-standard classes of function spaces and underlying measure spaces. In particular, our results are applied to any-order Sobolev embeddings in regular (John) domains of the Euclidean space, in Maz'ya classes of (possibly irregular) Euclidean domains described in terms of their isoperimetric function, and in families of product probability spaces, of which the Gauss space is a classical instance.

This paper addresses the problems of institutional changes in governance and the framing of biodiversity conservation policy at the level of the enlarged European Union. The current development of European Union governance has become more complex and multilevel, partially usurping competences from the central state and relying on networks of interconnected actors rather than on a hierarchy dominated and defi ned by the state. This shift is particularly challenging for biodiversity governance in new member states, where current decision making is still affected by post-socialist relations and massive ongoing institutional changes, often resulting in ineffi cient institutional designs and over-exploitation of natural resources. The paper offers a cross-country analysis of fi ve Central and Eastern European countries, characterized by different socialist regimes and different transition processes from hierarchical to democratic and market governance. The theoretical basis of the paper is institutional rebuilding in Central and Eastern Europe in the context of the emerging multilevel environmental governance of the EU. The data were collected from desk study research and interviews. The results show that some elements of multilevel governance existed in these countries prior to the transition, but that EU integration empowered lower levels of self-government. The mismatch between the old hierarchical institutions developed under socialism and the new decentralized institutions introduced during the transformation process still persists and is visible. The emergence of multilevel governance with multiple actors' participation is prone to create tensions, but evidence from the countries studied indicates that this is not necessarily a disadvantage. Copyright

Abstract:The European Union (EU) Water Framework Directive (WFD) requires EU member states to produce and implement river basin management plans, which are to be designed and updated via participatory processes that inform, consult with, and actively involve all interested stakeholders. The assumption of the European Commission is that stakeholder participation, and institutional adaptation and procedural innovation to facilitate it, are essential to the effectiveness of river basin planning and, ultimately, the environmental impact of the Directive. We analyzed official documents and the WFD literature to compare implementation of the Directive in EU member states in the initial WFD planning phase (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009). Examining the development of participatory approaches to river basin management planning, we consider the extent of transformation in EU water governance over the period. Employing a mixed quantitative and qualitative approach, we map the implementation "trajectories" of 13 member states, and then provide a detailed examination of shifts in river basin planning and participation in four member states (Germany, Sweden, Poland and France) to illustrate the diversity of institutional approaches observed. We identify a general tendency towards increased, yet circumscribed, stakeholder participation in river basin management in the member states examined, alongside clear continuities in terms of their respective pre-WFD institutional and procedural arrangements. Overall, the WFD has driven a highly uneven shift to river basin-level planning among the member states, and instigated a range of efforts to institutionalize stakeholder involvement-often through the establishment of advisory groups to bring organized stakeholders into the planning process.

Sobolev embeddings, of arbitrary order, are considered into function spaces on domains of R n endowed with measures whose decay on balls is dominated by a power d of their radius. Norms in arbitrary rearrangementinvariant spaces are contemplated. A comprehensive approach is proposed based on the reduction of the relevant n-dimensional embeddings to one-dimensional Hardy-type inequalities. Interestingly, the latter inequalities depend on the involved measure only through the power d. Our results allow for the detection of the optimal target space in Sobolev embeddings, for broad families of norms, in situations where customary techniques do not apply. In particular, new embeddings, with augmented target spaces, are deduced even for standard Sobolev spaces. RésuméOn considère des immersions de Sobolev d'ordre quelconque dans des espaces de fonctions sur des domaines de R n munis des mesures avec une tendance dans les boules qui est dominée par une puissance d du rayon. Des normes dans les espaces arbitraires invariants par réarrangements sont permises. Nous proposons une approche général basée sur la réduction des immersions en dimension nà des inégalités du type Hardy en dimension un. On souligne que ces inégalités dépendent de la mesure considérée seulement par le degré de puissance d. Notre résultat permets de détecter l'espace cible optimal dans les immersions de Sobolev, pour une large famille de normes dans des cas où le techniques habituelles ne s'appliquent pas. En particulier on déduit des nouvelles immersions avec espaces cible augmentés même dans le cas d'espace de Sobolev standard.Mathematics Subject Classification: 46E35, 46E30.holds for some constant C 2 and every f ∈ X(0, 1). The same characterization applies to any domain Ω with |Ω| < ∞, provided that the space W m X(Ω) is replaced with W m 0 X(Ω). This special case was earlier obtained, via a different approach, in [33]. Reduction principles for Sobolev type inequalities, for different kinds of norms or domains, are the subject of [3,29,30,31]. Compactness of Sobolev embeddings is characterized via reduction principles in [10,49].New results. In the present paper we abandon the point of view of linking Sobolev to isoperimetric inequalities, and pursue the approach to a wider family of Sobolev inequalities, via reduction principles, from a different perspective. A basic version of the inequalities that will be considered, called Sobolev trace inequalities in a broad sense, has the form u Y (Ω,µ) ≤ C ∇ m u X(Ω)

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Large inland floods represent a serious threat to the Central European territory. It is therefore necessary to develop efficient flood‐risk management based on shared responsibility, stressing the importance of the self‐engagement of local actors (such as municipalities, household, etc.). Central government flood expenditures are an influential factor that shapes their motivation and expectations. In this context, the article investigates the relevance of the concept of crowding out. In particular, it search for the reflection of the concept in the flood governance literature. A thorough review of Web of Science sources in the past 20 years has been undertaken in this matter. Furthermore, the intention is to discuss the problem of data availability (especially regarding flood expenditures of central governments) for assessing the crowding‐out effect on a macroeconomic basis. The Czech central government's activity after the disastrous floods of 1997 and 2002 is used as a case study.

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