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A fast approximation method to three dimensional equations in quasi-static uncoupled thermoelasticity is pro-posed. We approximate the density via Gaussian approximating functions introduced in the method approximate approximations. In this way the action of the integral operators on such functions is presented in a simple analytical form. If the density has separated representation, the problem is reduced to the computation of one-dimensional integrals which admit efficient cubature procedures. The comparison of the numerical and exact solution shows that these formulas are accurate and provide the predicted approximation rate 2, 4, 6 and 8., Funding Agencies|Universita degli Studi di Roma La Sapienza within the CRUI-CARE Agreement

A fast approximation method to three dimensional equations in quasi-static uncoupled thermoelasticity is pro-posed. We approximate the density via Gaussian approximating functions introduced in the method approximate approximations. In this way the action of the integral operators on such functions is presented in a simple analytical form. If the density has separated representation, the problem is reduced to the computation of one-dimensional integrals which admit efficient cubature procedures. The comparison of the numerical and exact solution shows that these formulas are accurate and provide the predicted approximation rate 2, 4, 6 and 8., Funding Agencies|Universita degli Studi di Roma La Sapienza within the CRUI-CARE Agreement

A fast approximation method to three dimensional equations in quasi-static uncoupled thermoelasticity is pro-posed. We approximate the density via Gaussian approximating functions introduced in the method approximate approximations. In this way the action of the integral operators on such functions is presented in a simple analytical form. If the density has separated representation, the problem is reduced to the computation of one-dimensional integrals which admit efficient cubature procedures. The comparison of the numerical and exact solution shows that these formulas are accurate and provide the predicted approximation rate 2, 4, 6 and 8., Funding Agencies|Universita degli Studi di Roma La Sapienza within the CRUI-CARE Agreement

A fast approximation method to three dimensional equations in quasi-static uncoupled thermoelasticity is pro-posed. We approximate the density via Gaussian approximating functions introduced in the method approximate approximations. In this way the action of the integral operators on such functions is presented in a simple analytical form. If the density has separated representation, the problem is reduced to the computation of one-dimensional integrals which admit efficient cubature procedures. The comparison of the numerical and exact solution shows that these formulas are accurate and provide the predicted approximation rate 2, 4, 6 and 8., Funding Agencies|Universita degli Studi di Roma La Sapienza within the CRUI-CARE Agreement

A fast approximation method to three dimensional equations in quasi-static uncoupled thermoelasticity is pro-posed. We approximate the density via Gaussian approximating functions introduced in the method approximate approximations. In this way the action of the integral operators on such functions is presented in a simple analytical form. If the density has separated representation, the problem is reduced to the computation of one-dimensional integrals which admit efficient cubature procedures. The comparison of the numerical and exact solution shows that these formulas are accurate and provide the predicted approximation rate 2, 4, 6 and 8., Funding Agencies|Universita degli Studi di Roma La Sapienza within the CRUI-CARE Agreement

Sobolev embeddings into Orlicz spaces on domains in the Eu-clidean space or, more generally, on Riemannian manifolds are considered. Highly irregular domains where the optimal degree of integrability of a func-tion may be lower than the one of its gradient are focused. A necessary and sufficient condition for the validity of the relevant embeddings is established in terms of the isocapacitary function of the domain. Compact embeddings are discussed as well. Sufficient conditions involving the isoperimetric function of the domain are derived as a by-product., Funding Agencies|Italian Ministry of Education, University and Research (MIUR) Prin 2017 "Direct and inverse problems for partial differential equations: theoretical aspects and applications"; GNAMPA of the Italian INdAM -National Institute of High Mathematics [201758MTR2]

Various notions of dissipativity for partial differential operators and their applications are surveyed. We deal with functional dissipativity and its particular case L-p-dissipativity. Most of the results are due to the authors., Funding Agencies|RUDN University Strategic Academic Leadership Program

Various notions of dissipativity for partial differential operators and their applications are surveyed. We deal with functional dissipativity and its particular case L-p-dissipativity. Most of the results are due to the authors., Funding Agencies|RUDN University Strategic Academic Leadership Program

Eigenvalue problems for the p-Laplace operator in domains with finite volume, on noncompact Riemannian manifolds, are considered. If the domain does not coincide with the whole manifold, Neumann boundary conditions are imposed. Sharp assumptions ensuring L-q- or L-infinity-bounds for eigenfunctions are offered either in terms of the isoperimetric function or of the isocapacitary function of the domain., Funding Agencies|Italian Ministry of Education, University and Research (MIUR) [2017AYM8XW, 201758MTR2]; GNAMPA of the Italian INdAM -National Institute of High Mathematics

Eigenvalue problems for the p-Laplace operator in domains with finite volume, on noncompact Riemannian manifolds, are considered. If the domain does not coincide with the whole manifold, Neumann boundary conditions are imposed. Sharp assumptions ensuring L-q- or L-infinity-bounds for eigenfunctions are offered either in terms of the isoperimetric function or of the isocapacitary function of the domain., Funding Agencies|Italian Ministry of Education, University and Research (MIUR) [2017AYM8XW, 201758MTR2]; GNAMPA of the Italian INdAM -National Institute of High Mathematics

Eigenvalue problems for the p-Laplace operator in domains with finite volume, on noncompact Riemannian manifolds, are considered. If the domain does not coincide with the whole manifold, Neumann boundary conditions are imposed. Sharp assumptions ensuring L-q- or L-infinity-bounds for eigenfunctions are offered either in terms of the isoperimetric function or of the isocapacitary function of the domain., Funding Agencies|Italian Ministry of Education, University and Research (MIUR) [2017AYM8XW, 201758MTR2]; GNAMPA of the Italian INdAM -National Institute of High Mathematics

Various notions of dissipativity for partial differential operators and their applications are surveyed. We deal with functional dissipativity and its particular case L-p-dissipativity. Most of the results are due to the authors., Funding Agencies|RUDN University Strategic Academic Leadership Program

Eigenvalue problems for the p-Laplace operator in domains with finite volume, on noncompact Riemannian manifolds, are considered. If the domain does not coincide with the whole manifold, Neumann boundary conditions are imposed. Sharp assumptions ensuring L-q- or L-infinity-bounds for eigenfunctions are offered either in terms of the isoperimetric function or of the isocapacitary function of the domain., Funding Agencies|Italian Ministry of Education, University and Research (MIUR) [2017AYM8XW, 201758MTR2]; GNAMPA of the Italian INdAM -National Institute of High Mathematics

Various notions of dissipativity for partial differential operators and their applications are surveyed. We deal with functional dissipativity and its particular case L-p-dissipativity. Most of the results are due to the authors., Funding Agencies|RUDN University Strategic Academic Leadership Program

Eigenvalue problems for the p-Laplace operator in domains with finite volume, on noncompact Riemannian manifolds, are considered. If the domain does not coincide with the whole manifold, Neumann boundary conditions are imposed. Sharp assumptions ensuring L-q- or L-infinity-bounds for eigenfunctions are offered either in terms of the isoperimetric function or of the isocapacitary function of the domain., Funding Agencies|Italian Ministry of Education, University and Research (MIUR) [2017AYM8XW, 201758MTR2]; GNAMPA of the Italian INdAM -National Institute of High Mathematics

Various notions of dissipativity for partial differential operators and their applications are surveyed. We deal with functional dissipativity and its particular case L-p-dissipativity. Most of the results are due to the authors., Funding Agencies|RUDN University Strategic Academic Leadership Program

The paper discusses new cubature formulas for the Riesz potential and the fractional Laplacian (-Delta)(alpha/2), 0 < alpha < 2, in the framework of the method approximate approximations. This approach, combined with separated representations, makes the method successful also in high dimensions. We prove error estimates and report on numerical results illustrating that our formulas are accurate and provide the predicted convergence rate 2, 4, 6, 8 up to dimension 10(4)., Funding Agencies|RUDN University Strategic Academic Leadership Program

We discuss conditions for Lipschitz and C-1 regularity of solutions for a uniformly elliptic equation in divergence form. We focus on coefficients having the form that was introduced by Gilbarg & Serrin. In particular, we find cases where Lipschitz or C-1 regularity holds but the coefficients are not Dini continuous, or do not even have Dini mean oscillation. The form of the coefficients also enables us to obtain specific conditions and examples for which there exists a weak solution that is not Lipschitz continuous.

We obtain a local estimate for the gradient of solutions to a second-order elliptic equation in divergence form with bounded measurable coefficients that are square-Dini continuous at the single point x = 0. In particular, we treat the case of solutions that are not Lipschitz continuous at x = 0. We show that our estimate is sharp., Funding Agency: RUDN University Strategic Academic Leadership Program

We deal with solutions of the Cauchy problem to linear both homogeneous and nonhomogeneous parabolic second-order equations with real constant coefficients in the layer , where and . The homogeneous equation is considered with initial data in , . For the nonhomogeneous equation we suppose that initial function is equal to zero and the function in the right-hand side belongs to , pamp;gt;n + 2 and . Explicit formulas for the sharp coefficients in pointwise estimates for the length of the gradient to solutions to these problems are obtained., Funding Agencies|RUDN University Program 5-100