61 research outputs found
On the blowup of multidimensional semilinear heat equations
No full textFilippas, Stathis; Liu, Wenxiong. (1991). On the blowup of multidimensional semilinear heat equations. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/1608
Quenching profiles for one-dimensional semilinear heat equations
No full textFilippas, Stathis; Guo, Jong-Shenq. (1991). Quenching profiles for one-dimensional semilinear heat equations. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/1676
Sharp trace Hardy-Sobolev-Maz'ya inequalities and the fractional Laplacian
No full textIn this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use them to produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants for various fractional Laplacians. In the case where the domain is the half space, our results cover the full range of the exponent (0, 1) of the fractional Laplacians. In particular, we give a complete answer in the L (2) setting to an open problem raised by Frank and Seiringer ("Sharp fractional Hardy inequalities in half-spaces," in Around the research of Vladimir Maz'ya. International Mathematical Series, 2010)
On a class of weighted anisotropic Sobolev inequalities
No full textIn this article, motivated by a work of Caffarelli and Cordoba in phase transitions analysis, we prove new weighted anisotropic Sobolev type inequalities where different derivatives have different weight functions. These inequalities are also intimately connected to weighted Sobolev inequalities for Grushin type operators, the weights being not necessarily Muckenhoupt. For example we consider Sobolev inequalities on finite cylinders, the weight being a power of the distance function from the top or the bottom of the cylinder. We also prove similar inequalities in the more general case in which the weight is a power of the distance function from a higher codimension part of the boundary
Correction to: Sharp Trace Hardy–Sobolev–Maz’ya Inequalities and the Fractional Laplacian
No full textCi siamo resi conto di un buco nella dimostrazione del Teorema 2 (iii) e 6 (ii) di [1].We became aware of a gap in the proof of Theorems 2(iii) and 6(ii) of [1] in the case
IMPROVING L^2 ESTIMATES TO HARNACK INEQUALITIES.
No full textWe consider operators of the form \mathcal L=-L-V, where L is an elliptic operator and V is a singular potential, defined on a smooth bounded domain \Omega\subset R^n with Dirichlet boundary conditions. We allow the boundary of \Omega to be made of various pieces of different codimension. We assume
that \mathcal L has a generalized first eigenfunction of which we know two-sided estimates. Under these
assumptions we prove optimal Sobolev inequalities for the operator \mathcal L, we show that it generates
an intrinsic ultracontractive semigroup and finally we derive a parabolic Harnack inequality up
to the boundary as well as sharp heat kernel estimates
Does Warfare Matter?: Severity, Duration, and Outcomes of Civil Wars
No full textDoes it matter whether a civil war is fought as a conventional, irregular, or symmetric non-conventional conflict? Put differently, do technologies of rebellion impact on a wars severity, duration, or outcome? We find that irregular conflicts last significantly longer than all other types of conflict, while conventional ones tend to be more severe in terms of battlefield lethality. Irregular conflicts tend to be won by incumbents, while symmetric non-conventional and conventional ones are more likely to end in draws. Substantively, these findings help us make sense of the evolution of civil wars, which are likely to become shorter, more intensely fought, and more challenging for existing governmentsbut also more likely to end with some kind of compromise between governments and armed opposition. Theoretically, our findings support factoring in the technology of rebellion (a variable capturing characteristics of conflicts that are visible at the micro level) when studying the severity, duration, and outcome of civil wars (macro-level patterns of conflicts); they also contribute a better understanding of the historical contribution of irregular war to both state building and social change.[electronic resource] :
Laia Balcells and Stathis Kalyvas.
ill.
Full text available through the CEACS repository
On Similarity Solutions of a Heat Equation with a Nonhomogeneous Nonlinearity
No full textAbstractWe are interested in positive radially symmetric solutions of the semilinear equationΔw−y·∇w2−Aw+|y|lwp=0,inRn,n⩾3, where p>1, l>−2 and A≡l+22(p−1). This equation is satisfied by self-similar solutions of a semilinear heat equation. We prove existence and non existence of solutions for various values of the parameters l and p. When solutions exist we study their asymptotic behavior and discuss their uniqueness. Our proofs are based on various continuity, comparison and Pohozaev type arguments
Corrigendum to “Optimizing improved Hardy inequalities” [J. Funct. Anal. 192 (2002) 186–233]
No full text- …
