Results 71 to 80 of about 5,210,310 (318)
Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
wiley +1 more source
Trace theorems on Herz-Morrey spaces with applications to Sobolev type inequalities
Boundary Value ProblemsIn this paper, we prove the trace theorems in the setting of Riesz potential operator for Herz-Morrey spaces and present some examples to illustrate the optimality of certain parametric conditions.
Abdul Hamid Ganie +4 more
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Approximation numbers of Sobolev embeddings of radial functions on isotropic manifolds
Journal of Function Spaces and Applications, 2007 We regard the compact Sobolev embeddings between Besov and Sobolev spaces of radial functions on noncompact symmetric spaces of rank one. The asymptotic formula for the behaviour of approximation numbers of these embeddings is described.
Leszek Skrzypczak, Bernadeta Tomasz
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Regularity for commutators of the local multilinear fractional maximal operators
Advances in Nonlinear Analysis, 2020 In this paper we introduce and study the commutators of the local multilinear fractional maximal operators and a vector-valued function b⃗ = (b1, …, bm). Under the condition that each bi belongs to the first order Sobolev spaces, the bounds for the above
Zhang Xiao, Liu Feng
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A Note on Sobolev‐Lorentz Capacity and Hausdorff Measure
Mathematische Nachrichten, EarlyView.ABSTRACT In this paper, we give an elementary proof that sets of zero p,1$p,1$‐Sobolev‐Lorentz capacity are Hn−p$\mathcal {H}^{n-p}$‐null sets, independently of nonlinear potential theory. We further show that there exists a set of Sobolev‐Lorentz‐(p,1)$(p,1)$ capacity equal to zero with Hausdorff dimension equal n−p$n-p$.
Daniel Campbell
wiley +1 more source
Geometric characterization of generalized Hajłasz-Sobolev embedding domains
Advances in Nonlinear AnalysisIn this article, the authors study the embedding properties of Hajłasz-Sobolev spaces with generalized smoothness on Euclidean domains, whose regularity is described via a smoothness weight function ϕ:[0,∞)→[0,∞)\phi :\left[0,\infty )\to \left[0,\infty ).
Li Ziwei, Yang Dachun, Yuan Wen
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Elliptic Problems with Additional Unknowns in Boundary Conditions and Generalized Sobolev Spaces
Axioms, 2021 In generalized inner product Sobolev spaces we investigate elliptic differential problems with additional unknown functions or distributions in boundary conditions. These spaces are parametrized with a function OR-varying at infinity.
Anna Anop +2 more
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Reproducing kernel Hilbert spaces on manifolds: Sobolev and Diffusion spaces [PDF]
Analysis and Applications, 2019 We study reproducing kernel Hilbert spaces (RKHS) on a Riemannian manifold. In particular, we discuss under which condition Sobolev spaces are RKHS and characterize their reproducing kernels.
E. Vito, Nicole Mücke, L. Rosasco
semanticscholar +1 more source
Relationship Between Limiting K‐Spaces and J‐Spaces in the Real Interpolation
Mathematische Nachrichten, EarlyView.ABSTRACT In the paper, “Description of the K$K$‐Spaces by Means of J$J$‐Spaces and the Reverse Problem,” Mathematische Nachrichten 296, no. 9 (2023), 4002–4031, we have established conditions under which the limiting K$K$‐space (X0,X1)0,q,b;K$(X_0,X_1)_{0,q,b;K}$, involving a slowly varying function b$b$, can be described by means of the J$J$‐space (X0,
Bohumír Opic, Manvi Grover
wiley +1 more source
Construction of Optimal Interpolation Formulas in the Sobolev Space [PDF]
, 2022 Kh. M. Shadimetov +2 more
openalex +1 more source