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Abstract: In this paper we consider the global gradient estimates for weak solutions of the parabolic -Laplacian type equation in a -Reifenberg flat domain. [Copyright &y& Elsevier]

Abstract: Under some assumptions on the continuous function , we obtain the local regularity of solutions of the strong -Laplacian by using the integral estimates in Campanato spaces. [Copyright &y& Elsevier]

Abstract: In this paper we develop a unifying method to prove the existence and uniqueness of weak solutions for the initial–boundary value problem of a non-uniformly parabolic equation. Some well-known parabolic equations are the special cases of this equation. [Copyright &y& Elsevier]

Abstract: In this paper we generalize gradient estimates in spaces to Orlicz spaces for weak solutions of second-order divergence elliptic equations with small BMO coefficients in Lipschitz domains. Our results improve the known results for such equations using the harmonic analysis method. [Copyright &y& Elsevier]

Abstract: In this paper we establish a stability result and an error estimate of weak solutions for the initial-boundary value problem of a generalized thin film equation and also obtain some higher regularity results for weak solutions. [Copyright &y& Elsevier]

This work studies an outstanding reaction–diffusion system modeling tumor invasion, with interactions among tumor tissue, acid concentration and normal tissue. This model has very different features from the models extensively studied in the mathematics literature. The most challenge issue for mathematical analysis of the present model is the existence of classical solution, since the diffusion of tumor tissue is influenced by the density of normal cells and diffusion degeneracy arises when normal cells are at the carrying capacity. A rigorous proof of global existence and uniqueness of classical solutions is presented. Moreover, we study global dynamics of the solution, and show asymptotic stability of the four possible constant equilibria under various scenarios. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we generalize gradient estimates in space to Orlicz space for weak solutions of elliptic equations of p-Laplacian type with small BMO coefficients in δ-Reifenberg flat domains. Our results improve the known results for such equations using a harmonic analysis-free technique. [Copyright &y& Elsevier]