Nonlinear Potential Theory and Weighted Sobolev Spaces

By Bengt-Ove Turesson. 2000

381 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3f6bf2b8152cc40855ca58efd59104b020700c36

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mechanics of Materials

Citations in the corpus

Manifold Constrained Non-uniformly Elliptic Problems (2019, neutral): “al Hausdorﬀ measure. • In the case Φ(x,t) ≡ tp(x) for p(x) ≤ n being a continuous function deﬁned on an open subset Ω, then HΦ falls in the class of the variable exponent Hausdorﬀ measures studied in [51, 61]. • In the case Φ(x,t) ≡ w(x)tp for p ≤ n and w(·) being a non-negative and measurable funct”
A remark on optimal weighted Poincar\'e inequalities for convex domains (2012, result): “For an insight into generalized Wirtinger inequalities, and more generally into weighted Hardy inequalities, we refer to [18, 21, 30], other results can be found for instance in [10, 11, 14, 16, 25].”
The Stokes operator in weighted Lq-spaces II: weighted resolvent estimates and maximal Lp-regularity (2007, background): “These extension operators Em have a common bounded extension E to a bounded extension operator from W 1,s (�) to W 1,s 0 (O) (see the explicit construction in [ 19 ]).”
Existence, uniqueness and optimal regularity results for very weak solutions to nonlinear elliptic systems (2016, neutral): “2 (See pages 229–230 in [43] and page 5 in [44]).”
User’s guide to the fractional Laplacian and the method of semigroups (2018, background): “Uk2 H1 a = kUk2 L2(Rn×(0,∞),yadxdy) +k∇x,yUk 2 L2(Rn×(0,∞),yadxdy). Since a∈ (−1,1), the weight ω(x,y) = ya belongs to the Muckenhoupt class A2(Rn×(0,∞)), see [41] for details about these weights and [44, 97] for weighted Sobolev spaces. Then H1 a is a Hilbert space with inner product hU,ViH1 a = Z∞”
Weighted Sobolev spaces and embedding theorems (2007, background): “ner product in the weighted space W1 2 (D,w) as: <u,v>= Z D ∇u·∇vw(x) dx, for any u,v∈W1 2 (D,w). Consider Dirichlet problem for the degenerate elliptic equation: div(w(x)∇u) = f, (1) u|∂D = 0. (2) in a bounded domain Dfor the weight w∈C1(D). Theorem 11. Let f∈L 2(D) and R D w(y)−n2 dx<+∞. ”
Diffusion phenomenon in Hilbert spaces and applications (2011, background): “Although a large class of weighted Sobolev inequalities can be found in [35] (pg.”
Recent developments in problems with nonstandard growth and nonuniform ellipticity (2021, background): “When Φ(x, t) ≡ w(x)t for p ≤ n and w(·) is a non-negative and measurable function, HΦ is of the type of the weighted Hausdorff measures in [207].”
Weighted Sobolev Spaces and Degenerate Elliptic Equations (2008, background): “For more informations about Ap weights see [11],[12], [26] and [27].”
Existence and regularity of maximal metrics for the first Laplace eigenvalue on surfaces (2013, background): “The Bessel capacity is equivalent to the variational capacity (see [42] Theorem 3.”
Fractional elliptic equations, Caccioppoli estimates and regularity (2014, background): “See [10, 12], also [31], for the theory of weighted Sobolev spaces.”