An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions by Emilia Bazhlekova

“…Existence, uniqueness and stability estimates in Sobolev spaces are established.…”
Get full text

Certain results for a class of nonlinear functional spaces by K. Soltanov, U. Sert

“…We prove embedding theorems, which indicate the relation of these spaces with the well known classical Lebesgue and Sobolev spaces with the constant and variable exponents.…”
Get full text

A note on linear elliptic systems on ℝ$^d$ by Ortner, C, Suli, E

“…We describe a variant of homogeneous Sobolev spaces, which are convenient for treating problems of this kind.…”

Partial regularity for BV minimizers by Gmeineder, F, Kristensen, J

“…This result extends the regularity theory for minimizers of quasiconvex integrals on Sobolev spaces to the context of maps of bounded variation. …”

On optimal control in a nonlinear interface problem described by hemivariational inequalities by Gwinner Joachim

“…Boundary integral methods lead to another HVI that is amenable to functional analytic methods using standard Sobolev spaces on the interior domain and Sobolev spaces of fractional order on the coupling boundary. …”
Get full text

The smoothness of solutions of the problems with nonlocal multi-point conditions for strictly hyperbolic equations by V. S. Il'kiv

“…We establish the solvability of this problem in the Sobolev spaces scale for almost all (except for the set of a given small measure) vectors of coefficients in the nonlocal conditions. …”
Get full text

Some results on statistics and functional data analysis by Dabo-Niang Sophie, Ah-Pine Julien, Llop Pamela, Yao Anne-Francoise

“…The first work decated to Multiple kernel SVM for classifying functional data in Sobolev spaces focus on optimization of the information from each derivatives of the original functions, the second work devoted to An input/output-based aggregation rule for functional data classification when the last is interested with the problem of regression if the functional data lives in a finite dimensionnal submanifold.…”
Get full text

Weak solutions for double phase problem driven by the (p(x),q(x))-Laplacian operator under Dirichlet boundary conditions by Mohamed El Ouaarabi, Chakir Allalou, Said Melliani

“… In the present paper, in view of the topological degree methods and the theory of the variable exponent Sobolev spaces, we discuss a Dirichlet boundary value problem for elliptic equations involving the $(p(x),q(x))$-Laplacian operator with a reaction term depending on the gradient and on two real parameters. …”
Get full text

Stability of the Steady States in Multidimensional Reaction Diffusion Systems Arising in Combustion Theory by Qingxia Li, Xinyao Yang

“…We prove that the steady states of a class of multidimensional reaction–diffusion systems are asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, paying particular attention to a special case, namely, systems of equations that arise in combustion theory. …”
Get full text

GEODESIC COMPLETENESS FOR SOBOLEV METRICS ON THE SPACE OF IMMERSED PLANE CURVES by MARTINS BRUVERIS, PETER W. MICHOR, DAVID MUMFORD

“…We show that the geodesic equation for Sobolev-type metrics with constant coefficients of order 2 and higher is globally well-posed for smooth initial data as well as for initial data in certain Sobolev spaces. Thus the space of closed plane curves equipped with such a metric is geodesically complete. …”
Get full text

Existence and decay of solution to coupled system of viscoelastic wave equations with strong damping in Rn by Keltoum Bouhali, Fateh Ellaggoune

“…The questions of global existence in the nonlinear cases is also proved in Sobolev spaces using the well known Galerkin method. …”
Get full text

Well-posedness of the free-surface incompressible Euler equations with or without surface tension by Coutand, D, Shkoller, S

“…We provide a new method for treating free boundary problems in perfect fluids, and prove local-in-time well-posedness in Sobolev spaces for the free-surface incompressible 3D Euler equations with or without surface tension for arbitrary initial data, and without any irrotationality assumption on the fluid. …”

On One Initial Boundary Value Problem for the Burgers Equation in a Rectangular Domain by M.T. Jenaliyev, M.G. Yergaliyev, A.A. Assetov, A.K. Kalibekova

“…Using the methods of functional analysis, priori estimates, and Faedo-Galerkin in Sobolev spaces and in a rectangular domain, we show the correctness of the initial boundary value problem for the Burgers equation with nonlinear boundary conditions of the Neumann type. …”
Get full text

On One Initial Boundary Value Problem for the Burgers Equation in a Rectangular Domain by M.T. Jenaliyev, M.G. Yergaliyev, A.A. Assetov, A.K. Kalibekova

“…Using the methods of functional analysis, priori estimates, and Faedo-Galerkin in Sobolev spaces and in a rectangular domain, we show the correctness of the initial boundary value problem for the Burgers equation with nonlinear boundary conditions of the Neumann type.…”
Get full text

On the singular behavior of solutions of a transmission problem in a dihedral by Hamid Benseridi, Mourad Dilmi

“…The considered problem is defined in a nonhomogeneous body of $\mathbb{R}^{3}$, this is done in the general framework of weighted Sobolev spaces. Using the results of Benseridi-Dilmi, Grisvard and Aksentian, we show that the study of solutions' singularities in the spatial case becomes a study of two problems: a problem of plane deformation and the other is of normal plane deformation.…”
Get full text

Semilinear multi-term fractional in time diffusion with memory by Nataliya Vasylyeva, Nataliya Vasylyeva

“…The key point in this approach is finding suitable a priori estimates of a solution in the fractional Hölder and Sobolev spaces.…”
Get full text

Navier-Stokes equations interacting with a nonlinear elastic solid shell by Cheng, C, Coutand, D, Shkoller, S

“…We prove existence and uniqueness of solutions in Sobolev spaces.…”

Fast spectral Galerkin method for logarithmic singular equations on a segment by Jerez-Hanckes, C, Nicaise, S, Urzua-Torres, C

“…Convergence rates of several orders are obtained for fractional Sobolev spaces He−1/2 (or H−1/200 ). Main tools are the approximation properties of the discretization basis, the construction of a suitable Hilbert scale for weighted L2-spaces and local regularity estimates. …”

Heat Kernels Estimates for Hermitian Line Bundles on Manifolds of Bounded Geometry by Yuri A. Kordyukov

“…The proof is based on some tools from the theory of operator semigroups in a Hilbert space, results on Sobolev spaces adapted to the current setting, and weighted estimates with appropriate exponential weights.…”
Get full text

Existence results for Schrödinger type double phase variable exponent problems with convection term in $ \mathbb R^{N} $ by Shuai Li, Tianqing An, Weichun Bu

“…We gave the corresponding Musielak-Orlicz Sobolev spaces and proved certain properties of the double phase operator. …”
Get full text