Search results for "solution"
showing 10 items of 5638 documents
Projective resolutions associated to projections
2000
In this paper we will describe projective resolutions of d dimensional Cohen–Macaulay spaces X by means of a projection of X to a hypersurface in d+1-dimensional space. We will show that for a certain class of projections, the resulting resolution is minimal.
On the interior regularity of weak solutions to the 2-D incompressible Euler equations
2016
We study whether some of the non-physical properties observed for weak solutions of the incompressible Euler equations can be ruled out by studying the vorticity formulation. Our main contribution is in developing an interior regularity method in the spirit of De Giorgi–Nash–Moser, showing that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity result $$\begin{aligned} u \in L_\mathrm{loc}^{2+\varepsilon }(\Omega _T) \implies \mathrm{local\ regularity} \end{aligned}$$ for weak solutions in the energy space $$L_t^\infty L_x^2$$ , satisfying appropriate vorticity estimates. We also obtain impr…
Nonlinear balayage on metric spaces
2009
We develop a theory of balayage on complete doubling metric measure spaces supporting a Poincaré inequality. In particular, we are interested in continuity and p-harmonicity of the balayage. We also study connections to the obstacle problem. As applications, we characterize regular boundary points and polar sets in terms of balayage. Original Publication:Anders Björn, Jana Björn, Tero Mäkäläinen and Mikko Parviainen, Nonlinear balayage on metric spaces, 2009, Nonlinear Analysis, (71), 5-6, 2153-2171.http://dx.doi.org/10.1016/j.na.2009.01.051Copyright: Elsevier Science B.V., Amsterdam.http://www.elsevier.com/
Nonlinear scalar field equations with general nonlinearity
2018
Consider the nonlinear scalar field equation \begin{equation} \label{a1} -\Delta{u}= f(u)\quad\text{in}~\mathbb{R}^N,\qquad u\in H^1(\mathbb{R}^N), \end{equation} where $N\geq3$ and $f$ satisfies the general Berestycki-Lions conditions. We are interested in the existence of positive ground states, of nonradial solutions and in the multiplicity of radial and nonradial solutions. Very recently Mederski [30] made a major advance in that direction through the development, in an abstract setting, of a new critical point theory for constrained functionals. In this paper we propose an alternative, more elementary approach, which permits to recover Mederski's results on the scalar field equation. T…
Continuous numerical solutions of coupled mixed partial differential systems using Fer's factorization
1999
In this paper continuous numerical solutions expressed in terms of matrix exponentials are constructed to approximate time-dependent systems of the type ut A(t)uxx B(t)u=0; 0 0, u(0;t)=u(p;t)=0; u(x;0)=f(x);06 x6p. After truncation of an exact series solution, the numerical solution is constructed using Fer’s factorization. Given >0 and t0;t1; with 0<t0<t1 and D(t0;t1)=f(x;t); 06x6p; t06t6t1g the error of the approximated solution with respect to the exact series solution is less than uniformly in D(t0;t1). An algorithm is also included. c 1999 Elsevier Science B.V. All rights reserved. AMS classication: 65M15, 34A50, 35C10, 35A50
Nonexistence of global weak solutions for a nonlinear Schrodinger equation in an exterior domain
2020
We study the large-time behavior of solutions to the nonlinear exterior problem L u ( t , x ) = &kappa
Fixed Points for Multivalued Weighted Mean Contractions in a Symmetric Generalized Metric Space
2020
This paper defines two new concepts: the concept of multivalued left-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space and the concept of multivalued right-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space, and demonstrates fixed-point theorems for them. For these, we demonstrated two fixed-point existence theorems and their corollaries, by using the properties of the regular-global-inf function and the properties of symmetric generalized metric spaces, respectively. Moreover, we demonstrated that the theorems can be applied in particular cases of inclusion systems. This article contains …
Positive solutions for the Neumann p-Laplacian
2017
We examine parametric nonlinear Neumann problems driven by the p-Laplacian with asymptotically ( $$p-1$$ )-linear reaction term f(z, x) (as $$x\rightarrow +\infty $$ ). We determine the existence, nonexistence and minimality of positive solutions as the parameter $$\lambda >0$$ varies.
A construction of equivariant bundles on the space of symmetric forms
2021
We construct stable vector bundles on the space of symmetric forms of degree d in n+1 variables which are equivariant for the action of SL_{n+1}(C), and admit an equivariant free resolution of length 2. For n=1, we obtain new examples of stable vector bundles of rank d-1 on P^d, which are moreover equivariant for SL_2(C). The presentation matrix of these bundles attains Westwick's upper bound for the dimension of vector spaces of matrices of constant rank and fixed size.
Perturbed eigenvalue problems for the Robin p-Laplacian plus an indefinite potential
2020
AbstractWe consider a parametric nonlinear Robin problem driven by the negativep-Laplacian plus an indefinite potential. The equation can be thought as a perturbation of the usual eigenvalue problem. We consider the case where the perturbation$$f(z,\cdot )$$f(z,·)is$$(p-1)$$(p-1)-sublinear and then the case where it is$$(p-1)$$(p-1)-superlinear but without satisfying the Ambrosetti–Rabinowitz condition. We establish existence and uniqueness or multiplicity of positive solutions for certain admissible range for the parameter$$\lambda \in {\mathbb {R}}$$λ∈Rwhich we specify exactly in terms of principal eigenvalue of the differential operator.